The Lord of Chaos in that useage is representative of an inversion of proper order. Among the details of the celebrations of that feast include the highest-ranking people serving the lowly and the lower-classes giving orders to their superiors. The Lord of Chaos gives ridiculous commands which have to be followed, and it's all in a spirit of fun, with everyone knowing that tommorrow it all goes back to normal.

Throughout the book "Lord of Chaos" we see an inversion of order. One of the Forsaken is collared and bound as a servant; a Queen is treated as an honored guest when she is actually a captive; the enemies of the Dragon Reborn strike at him in the guise of friendship (Taim building the Black Tower; Niall stirring up the Dragonsworn; Sevanna planning to take Radn to marry him & use him to unite the Aiel behind her); an Amyrlin is raised to be a puppet for those who 'follow' her; Mat is going to take command of an army with the leaders of that army believing he is simply going to be a figurehead appointed through his friendship with Rand, while he & Rand know that his leadership of the army is going to be false threat that will not be truly responsible for the fight against Sammael; the Aes Sedai, traditionally the ones who keep male channelers down, and the ones who make the kings bend to their will, fall under the heel of an army of male channelers and kneel & swear to a man. We also see Graendal and learn of her propensity for making slaves out of high-ranking and powerful people.

The theme of false leaders or leaders in inverted situations or circumstances runs throughout the book. The one concrete order we know the Dark One gives the Forsaken is to keep their hands off of Rand. By "letting the Lord of Chaos rule" they secretly are treating Rand as a figure of derision whose apparent dominion they hold in contempt, because very soon, it will be over, just as the Lord of Chaos is dethroned when the Feast of Fools ends. That speaks of the strategy of the Shadow - to let Rand get bogged down trying to rule the world while they freely run hither and yon like Satan in the Book of Job causing trouble and stirring up unrest and strife. This makes Rand's rule more difficult and consumes more of his attention - a Dragon who is trying to reform the tax codes when Tarmon Gaidon breaks out is going down.

We will later see in tPoD, Moridin's ramblings over his game and the abilities of the Fisher seem to reflect this mentality. When the Fisher (Rand) is strong and powerful, he is also slow and ponderous. Rand articulates a similar idea in his last conversation in that same book when he tells Min that he is going off on his own as a change of tactics. In the NEXT book, we see this manuever of Rand's has set the Shadow to worry far more than his conquests did. After all, those conquests only struck at the world, and their rivals. They always knew exactly where he was and what he was up to. He was predictable and containable as long as he was playing worldly power games and trying to rule nations. When he leaves behind his thrones and armies, and goes off the grid, suddenly they are all a-tizzy because he could be doing ANYTHING. He has gone from being the Evil Empire to Osama bin Laden, capable of striking anywhere at any time. The "let the Lord of Chaos rule" strategy was intended to avoid exactly that - Rand was supposed to stay high-profile and plod across the land at the head of an army, so they could see what he was up to and prevent him from doing anything seriously harmful to the cause. If, for instance, he had still be playing the king-general when they learned of his intent to cleanse saidin, they would know exactly where to get him and stop him. As it is, until he actually activates the Choedan Kal, they cannot do the first thing to stop him, and by that time it is too late.

There might also be metaphysical reasons which we don't have enough information to fully explain, but can guess at, such as the stresses and strains of leadership have done more than any other single factor to turn Rand as far to the dark side as he went in tGS. Note as well, that he has not struck any blows against the Shadow nearly as significant as the Cleansing since he resurfaced and went back to being the high and mighty Dragon Reborn, but was almost swayed into doing the Shadow's work for it.