As far as I know, the Teamsters don't unionize university workers. You know, the UAW doesn't unionize Postal Workers. Jeez.
That's exactly what was said in the article. The NLRB said they had the right to vote to unionize or not. That union is specific to university employees and negotiates, apparently, for several different branches of workers.
It's not a good thing but it is a coming thing. It'll be difficult for the NLRB to deny any school that petitions and some will unionize and some won't.
It's just another step toward "players are employees" and it sucks, but it's coming.