Several months ago I bought Sonic the Hedgehog (1) on iOS and was very happily surprised to see it appear on my 4th gen Apple TV also. Now I bought Sonic 2 but it hasn't shown up on the Apple TV yet.
I checked that it is one of the Sonic games with an Apple TV counterpart, so it is possible.
In the Apple TV menu I went to Settings > Apps > Automatically Install Apps and switched it to "On" (I guess it was off when I purchased Sonic 2, but not 1). I then restarted the Apple TV but no new apps appeared.
I also tried switching accounts and switching back, hoping that would prompt tvOS to check for available downloads, but it didn't.
How can I get iOS apps with an Apple TV version to install on Apple TV? Thanks.