Game companies say it is too early to predict how university administrations will become involved in e-sports.

“This is just how basketball was in the 1940s,” said Christopher Wyatt, senior manager for North American publishing at Riot Games. “A lot of the structure and organization you see in more formal athletics, that groundwork is still being laid down here.”

But it is unclear whether becoming a more formal part of a school would help or harm the growth of college e-sports. The time commitment required for serious competitive gaming could lead to concerns about whether e-sports leave enough time for academic study. In addition, formal recognition could diminish the autonomy that companies and teams have on campuses, bringing about rules like Title IX, the gender equity law.

About the possibility of more official recognition, Dr. Taylor said, “I don’t think collegiate e-sports players are unified in any way that this is a good thing.”

For game developers, however, the lure of being on campus is simple.

“We think that’s where a lot of our players are,” said Michael Morhaime, the chief executive and co-founder of Blizzard Entertainment, which develops and publishes entertainment software.

In September, Blizzard flew eight finalists from the College of Staten Island, University of Massachusetts-Amherst and other colleges to Seattle to compete for $5,000 in scholarship money in a tournament of Hearthstone, a virtual card game from the company. Last year, Azubu, a games media company, sponsored a competition that awarded $40,000 in prize money to six students on a StarCraft II team from the University of California, Berkeley.

Last February, Riot Games hosted its first North American Collegiate Championship, something like the Final Four for League of Legends, Riot’s popular online battle game. A team of five students from the University of Washington won in front of a roaring audience at an e-sports studio that Riot operates in Manhattan Beach, Calif., with 169,000 more people watching online at the tournament’s peak.