TINLEY PARK, Ill.—Sean Bensema stayed up late one recent evening practicing and woke up unusually early the next morning to prepare for the biggest moment of his life: a tryout for an athletic scholarship to college.

The shaggy-haired 18-year-old didn't need to change out of the T-shirt he slept in or even leave his parents' house to make the squad. He just set up his laptop on the dining-room table and started stunning his enemies with fire shot from the hands of his digital avatar.

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