Perhaps it is best to watch "Leeroy!!" video before learning about the humor shown while Leeroy Jenkins is still AFK (away from the keyboard).
The fact is that the plans being discussed were meant as a complete joke to those very familiar with the game, and so Leeroy Jenkins is not the downfall of the group. If you don't know what "Divine Intervention" does, read on.
It may go without saying that it is easier for a group of combatants to fight a smaller number of enemies per battle, even at the cost of needing to fight more battles if needed. A group of fighters does not generally benefit, while fighting some enemies, to have even more enemies join the battle and having the additional foes help the original batch of enemies by inflicting damange before the first enemies are fully dealt with. Also having more enemies at once can be relatively more chaotic. Also, game mechanics in World of WarCraft let several benefits occur only when players are not actively in battle, including faster restoration of health and mana points (with and even without eating and drinking), undisturbed spell casting that allows for easier healing, and the possibility for priests and paladins to cast resurrection spells that give life back to players who are dead.
A big, huge, and too often not recognized joke derives from the fact that the eggs only hatch when they are not left undisturbed. Disturbing multiple eggs at once at the start of a battle, or arousing eggs during a battle, will cause more dragonlings to hatch and fight the players before the battle can complete. From this, the "plans" being made have several details that will cause the exact opposite effect of what is desired.
Speculation is that damange may awaken the eggs. The "AoE" (and also further abbrevaited in the video as "AE") spells that have a wide "area of effect" will do less damage to the small number of unhatched dragonlings than the alternative attacking spells that have more concentrated damage done to a single enemy. Much worse is the fact that the wide-area attacks will cause minor damage to the unhatched eggs, disturbing the eggs. More enemies will hatch early on and join the fray.
What I have been able to find from multiple sources is that running over the eggs definitely causes them to spawn hatched dragonling enemies. Once it is decided that the room will be entered, the planner states he will gather all of the eggs. Indeed, true to his word, once he does enter the room, I do not see a lot of weapon swinging occuring at the already hatched dragonlings.
"Intimidating Shout" causes a "fear effect" in enemies that will cause them to temporarily flee the area, making them difficult for the Paladins to fight as they are scattered. This skill could be useful towards the end of a fight to buy some time so that wounded allies can be healed, but nobody is going to need excessive healing at the very beginning of the fight. When scattered, the fully afraid enemies (which will have purple skull icons over their heads, as seen in the video) will try to attract any of their allies, so after the fear effect wears off the enemies will re-convene along with their newly attracted allies, so there will be an even larger group, which is the exact opposite effect of that the "plans" state are desired. The planner intends to do this as much as possible until his "Shouts are done", and after he has exhausted this ability to worsen the situation himself, instructions are given for others to take turns multiplying their troubles by doing the same.
Also, combining this with the earlier plan, of using area of effect spells, is terrible. It is better to have a small area be attacked by all the mages, and to have all of the enemies in that small area so each enemy gets hurt by multiple mages. By having the enemies scattered, as the individual players select one enemy to attack, each attacked enemy will be attacked fewer spells, perhaps by just one mage. Furthermore, the area around each attacked enemy will be attacked, and since the enemies are scattered, this means several different areas will be attacked. Instead of one wide area of effect being attacked, which was downtalked in the last bullet point, there will instead be several wide areas attacked, so there will just be that many more eggs that will be disturbed.
The last-ditch skill "Divine Intervention" kills whoever casts it. In case this isn't abundantly clear, I'll state it again simply: The Paladin dies. (That word, "dies", is not very healthy.) The "Divine Intervention" jokes require, for their humor, a knowledge of how the skill works. As the in-game description states, "The paladin sacrifices himself". The targetted ally "cannot take any action" while affected by Divine Intervention. This is a disaster that is mentioned, but not explained, in the video. Statements made in the video regarding being unable to move at all, and being unable to cast any spells, are the expected result of Divine Intervention.
Why would anyone use Divine Intervention? This shield aids "the protected party member, who will be immune to all harmful attacks". This additionally causes the shielded target to magically lose any of the "aggro" (aggrevation) and/or "threat" generated through battle. Computer-controlled enemies will therefore leave the shielded target alone for a short time period. If this is done at the end of the battle, the enemies will see no threatening target to attack. Computer-controlled enemies will then actually conclude that the battle is finished and they will leave the battle scene, returning to their original locations before they were attracted into the battle (perhaps by an afraid monster due to an earlier bullet point mentioned). This can work great when properly used: If a Paladin is low on health and knows he is definitely about to die in battle anyway, he can sacrifice his life, which he knows he is about to lose anyway, and cast this shield on another player who can then live and later, after the battle, resurrect the dead players (including the Paladin that cast Divine Intervention). There is also a limitation of a Paladin being unable to cast the spell (after being resurrected from the dead) within one hour of the last time the Paladin had cast the spell, so this one-hour "cooldown" period is yet another reason why Divine Intervention may be used sparingly.
Separately, it is worth noting that game mechanics (that determine who can taunt to get attention) exist to help cause monsters to fight players wearing the heaviest armor first, so logically, if monsters are too busy focused on those with heavy armor first, this means the monsters end up leaving less armored player characters (like mages) alone. This lets mages attack from a distance without having their spellcasting being continuously slowed down by the interruption of being hit. This also minimizes any problems from a mage's limitation of only wearing the light-weight cloth armor-type in the game (like the Divine Mantle shoulderpads), and not being able to survive many hits compared Paladins, who can have much damage absorbed by the strongest armor-type in the game that Paladins crave and wear. This, the fact that mages generally don't get attacked so early in a fight, also means the still-unattacked mages simply won't need any sort of magical shield. This will be especially true during if the monsters are not attacking during part of the time that the shield will last, and the monsters won't be very busy attacking if they are instead running away wildly (and calling in re-inforcements) due to being impacted by an Intimidating Shout skill as an earlier disasterous plan metnions.
The plan to cast Divine Intervention on the mages, as mentioned in the video's discussion, is probably what leads to the plans being referred to as having "impossible" game mechanics (to have mages attack with area of effect spells when they are shielded), but largely is simply another example of the plans simply not working, and in fact causing an effect opposite to what is planned. If this plan gets executed, then the mages will receive a useless shield, the (lousy) plan of having mages cast "area of effect" spells early will become temporarily impossible. When the Divine Intervention shields runs out, the mages could in theory execute the disasterous plan of casting area of effect spells then. If the battle is already over (that is, if all of the players died except those protected by the stupid use of Divine Intervention shields), living mages will not have any magical spells that resurrect other players from the dead (which is a key reason why mages generally aren't the selected target to receive a Divine Intervention shield even when the skill is properly used, towards the end of a fight).
To people unfamiliar with this area of the game, it may look like the player who recorded the video is trying to run from trouble, and everywhere he turns he simply finds more trouble, and that this is all Leeroy's fault. That just isn't the case.
The player that the camera watches clearly tryies to run through eggs, waking them up as much as he can. This isn't talked about in the video, but efforts to make sure eggs get trampled on are clearly visible when a viewer knows to look for this. What may originally look like a random turn is, when people understand this, actually an intentional effort to make sure that eggs are trampled on instead of accidentally being narrowly avoided. The player is too busy complaining endlessly about Leeroy that he doesn't fight any of the monsters, and instead he spends his time running around trampling eggs, making the situation worse and worse as he continues to complain about how Leeroy caused a little bit of trouble at the beginning.
At one point, the player he looks like he is actually leaving the dangerous deadly center by running up a ramp. This potential escape looks like the player's only chance to possibly, maybe, if he is lucky, survive, if he can handle the monsters at the top of the ramp and if the monsters below the ramp focus on only other players and if those monsters, after killing the other players, forget about the player that ran up the ramp. Even that possibility is rather doubtful. However, the player only runs up the ramp long enough to attract further trouble. Once the enemies at the top of the ramp see him, he jumps off of the ramp and back into the fray below the ramp. The enemies at the top of the ramp are now running down the ramp to join the fight.
In summary, Leeroy was not some jerk that ruined an excellent plan by expert players. Leeroy could have very rightly concluded that fighting a small group of monsters by his lonesome self, with approximately a 0% chance of success, would be a more likely way for him to survive than what the planners came up with. The video didn't just show a group "meticulously and statistically plan out" a method of victory, but rather, the meticulous effort in creating the plan was not actually helping, at all. If there is a commentary that the video is trying to make, that is perhaps it: Excessive planning is not always needed, and furthermore can be not helpful, and can be even be completely useless. Whether the video was trying to make that statement or not, there were undeniably a great number of jokes about Leeroy's group that may not have been understood (and so not even noticed) at all by many, if not most viewers to date. Myself would be included, in fact, if I didn't have a friend point out some of the game mechanics I wasn't aware of.