“At night, I dream about Dota,” he said. “Sometimes I dream I’m a Dota hero.”

The game — its name is an acronym for Defense of the Ancients — is played on a square map with passages for players between enemy bases. Players pick game avatars from a cast of more than 100 heroes, each with a different set of strengths and weaknesses. To win the game, players must work as a team to destroy an enemy structure called an Ancient, while dodging various defenses, marauding monsters called creeps and other players.

Using a microphone connected to his computer, Mr. Dager spoke to teammates in a quiet, steady voice, using an argot that would be incomprehensible to nongamers. Evil Geniuses won its first two scrimmages of the day. During a third match, though, one of his teammates seemed to lose focus and the other team began building up a large lead. Mr. Dager lost patience.

“I can’t play Dota this way,” he said to the player. “What you’re doing makes no sense. Just follow your teammates.”

Normally, when he finishes practicing, Mr. Dager streams hours of informal matches with other players on Twitch, sometimes to as many as 9,000 viewers. He spent less time on Twitch in recent days to rest up ahead of a trip to China this week for a tournament, one of about 10 he will attend around the world this year.

In Mr. Dager’s view, the physical barriers to becoming an e-sports athlete are far lower than for conventional sports. He lists fingers and a brain as the primary tools people need to get started. What most people lack, he said, is a singular focus on games, a willingness to clear away all other distractions.

His obsession with video games was a sore point with Mr. Dager’s parents during his teenage years, as it was for the parents of many top gamers.

“I, and many players like me, sacrificed everything,” said Mr. Dager, who is almost a senior in college but is not attending school now. “We gave up on sports and friends and school just so we can play more.”