It is interesting how people can interpret things differently. I know nothing about the situation, but I do happen to be an antitrust expert. So, let me offer a couple uninformed opinions just for fun:
First, Varsity may be trying to offer a benefit to the participants by arranging availability at hotels, perhaps even at a reduced rate. In return, the hotels may be asking Varsity for some effort to direct participants to them, perhaps in exchange for that reduced rate. If so, that could be a win for all the parties involved, especially if the alternative is limited hotel availability at higher rack rates.
The Cheerleading as a sport thing is very interesting and complicated. Some do not want it to be classified as a sport because they are worried schools would use it as a title 9 offset to football and then reduce investment in other sports for women and girls. Others want it to be classified as a sport so that it is covered by insurance schools take out on their sports programs. So this is a very complicated issue, as least as I understand it.
Best.