Yes, the Apple TV fourth generation supports third-party gaming controllers equipped with Bluetooth 4.0.
Apple has said the all-new Apple TV is designed with "serious" gamers in mind. The company seeks to disrupt the console market by opening tvOS to developers. Among the many apps that have been created for the Apple TV 4, games are definitely a highlight.
The Siri Remote can also be used as a game controller thanks to its touch pad, built-in accelerometer, and gyroscope.