No, it's BLM land and first come, first served. However, it's a lot of BLM land and space isn't an issue.
The event usually is pretty close to the same spot each year. Greg's trailer is ground zero and folks make a choice if they want to be close to the main campfire area or be part of the snob hill crowd.
Park where you want.
There's no restriction on what kind of trailer parks next to you but the Escapes do seem to park in proximity to each other with a mix of SOB, Casita's being one of the dominant brands.