Apple TV is a decent mobile gaming device, but if you are thinking of using it as an Xbox or PlayStation alternative then you will be disappointed. Despite the $200 price tag, Apple TV is not for serious gaming.
The 64 bit A8 chip is not powerful enough to compete with Xbox or PlayStation. Games like Asphalt 8 were jittery on the device, but I am suspecting a software bug as it’s the same chip used in iPhone 6 and iPad Mini 4.
From the game selection point of view, there are great mobile games in the App Store but nothing powerful enough to appeal to a PC gamer.