Game controller

If you have an Apple TV HD box or Apple TV 4K box, then your TV brand doesn’t matter.

If you have the Apple TV app among the apps on your smart TV, then that doesn’t give access to Apple Arcade.

If you have an Apple TV HD box or Apple TV 4K box, then you can connect one or more of these wireless game controllers:

Connect a wireless game controller to your Apple device - Apple Support.

Note that this list doesn’t include the latest versions of Xbox or PS controller (yet). Two compatible controllers are currently also re-sold through Apple. Game controllers - Remotes & controllers - Apple TV accessories - Apple Store online

To connect: Use Bluetooth accessories with your Apple TV - Apple Support

Pretty sure Apple Arcade does not work with non apple devices even if they support the appletv app