HYDERABAD, India—The Bangalore Warhawks had a lot riding on a game earlier this month. For starters, Bob, a 55-year-old retired dentist from Los Angeles, was in the stands watching, and they really wanted to impress him.

The Warhawks are part of a fledgling American football league set up in South Asia two years ago by a California couple and investors including actor Mark Wahlberg and NFL Hall-of-Famers Mike Ditka and Michael Irvin.

...