It seems to me the group (as a whole) did get to the campground before you did, and claimed their sites. Maybe the whole question boils down to whether the group is treated as a single party or as several individual parties when it comes to claiming specific sites that they had reserved. You seem to be of the opinion that they're a group of individual parties, while the host apparently decided that they're a single party spanning multiple sites. I don't know if there's one correct answer, nor what the official opinion of the state is; both options seem like they could be reasonably defended.
I must say it seems like a strange hybrid of reservations and first-come, first-served camping. The only time I've encountered anything like this system is at Denali Tek campground, but at least there the sites are all about the same size and all sufficiently large for any RV they permit to camp there.
