His best-known concept was the Temporary Autonomous Zone, a sort of short-lived bubble of alternative reality where humans could live as they were supposed to, free of oppression. Burning Man is a TAZ, or was thought to be, it may have accumulated too much structure by now. A party is a TAZ, partly because (as Prince sang) they aren't meant to last.
I think it's a mistake to take Hakim Bey too literally. They say Burning Man is a TAZ, and far be it from me to say otherwise, but it's not one which does me much good. Burning Man is hard to get to, and while it might have been pure anarchy in its early days, it has become unavoidably institutionalized, a place of rules and regularities.
One fascinating thing about Burning Man is that it is on one level this amazing chaotic party, but also highly highly organized, in a particularly hippie-inflected way. This is a very large handbook for DPW workers which gives some sense of the organizing methodolgy.