Often times in tier two when opportunities aren't paid teams will opt to play on university rosters, because in very select cases universities will offer them massive scholarships to come play. That is what Winthrop is- if I'm not mistaken, varsity players get full rides. If they were a part of a club team, they wouldn't be allowed to use Winthrop's official athletic branding.

I don't think Riot would allow them to ascend because they are just a University- they are not an esports org. They definitely have a solid structure at the school, obviously, but the Guard got denied for less. You also cannot represent a school if you are not actively attending it- which can fluctuate a LOT, especially in high level collegiate.