Comcast Corp.’s NBC Sports on Wednesday said it would televise an esports tournament later this summer, the latest broadcaster turning to competitive videogaming to grow viewership at a time when many consumers are cutting the cord.

The cable network hopes a tournament built around a popular quirky game called “Rocket League” will attract hard-to-reach viewers—particularly younger males—who increasingly are ditching cable subscriptions for live-streaming services such as Netflix Inc.

NBC...