Trying to figure out the anti-trust violations in this. The NCAA doesn't require a school to be part of it for the school to have a football team. There are a number of college football organizations. If the NCAA kicks you out there is nothing to prevent you from forming your own football organization. There is no restrain of trade, the schools are free to get their own TV contracts, etc.
There has been talk for years about the upper level schools going out of their own separate from the NCAA for a number of years. If they did what can the NCAA do to stop them?
This is not the analysis used for antitrust violations. Instead:
(1) Define the market: in this case, the market for college athletes' services is a pretty easy market to see;
(2) Determine market share: the NCAA has the overwhelming share;
(3) Determine the litigant's market power (for markets that have more contested market shares, this analysis often turns on the litigant's ability take action that significantly impacts market pricing): with the overwhelming share of the market, the NCAA wields massive market power;
(4) Is the litigant using its (the NCAA's overwhelming) market power in anti-competitive ways, i.e., restricting competition for those college athletes' services? The argument in favor of giving more to the athletes says yes.
Where the NCAA fights its fight is primarily directed at defining the market (1). The NCAA says there is no college athletes' services market if there is no amateur college athletics--that amateurism is what makes the market. This argument has generally not gone well for the NCAA.
The NCAA also says that its restrictions are to the benefit of all college athletes (4), providing benefits to them that, without its set of rules to set an even playing field across college athletics, would not be available. You could call this the goose with the golden eggs theory.
Also, upon reading that text, it looks like the law is designed to establish a players' union to negotiate with the NCAA and member institutions over the player contracts.