When Anthony Hasson isn’t lifting weights at Wyandotte Athletic Club in Columbus, Ohio, he’s there dodging arrows and slicing bananas. The 27-year-old’s fitness routine has changed since the gym added virtual-reality headsets and videogames last year.

“You don’t even realize you’re getting a workout until you’ve been going 20 or 30 minutes straight,” says Mr. Hasson, an auto mechanic who estimates he has lost at least 5 pounds as a result of adding the practice to his twice-weekly workouts. “It’s definitely the future of...