Varsity only college esports tournaments are really odd. reasons schools would like to compete against each other include.......geography, rivalry, instutional history, both are good, academics, etc. ¯\_(ツ)_/¯ the label "varsity" as defined by a tournament organizer is odd.
Even odder to have a varsity designation without a paid coach... Correct me if I am wrong, but seeing any collegiate physical sport without a paid coach would be beyond rare. I personally don’t know of any occurrence where that is the case.