Zynab Makki, a junior at Champlain College in Burlington, Vt., had driven 90 minutes from her home for the chance to meet Tyler Schrodt, the young founder and chief executive of the Electronic Gaming Federation.

Since he started the E.G.F. out of his dorm room four years ago, Schrodt has branded himself as the one-stop guru for college students hoping to coax their overflowing video-game clubs from the fringes of university life toward a more mainstream existence. He presents his gaming federation as part mentor and part support system — “the Swiss Army knife for esports on campus.”

His true goal, though, and that of several other organizations jockeying for leadership roles in the growing but haphazardly governed world of college gaming, is bigger: to organize a sort of N.C.A.A. for esports.

That grand ambition means regular meetings with skeptical university officials but also sit-downs with students like Makki, who runs a club that hopes to persuade Champlain to grant it varsity status. She arrived at Schrodt’s office in Manhattan over the summer armed with questions about sponsorships, scholarships and strategy.