If Apple have been working on this as long and as hard as it seems then they may of thought about this. I do really believe that the Apple TV needs more functions, an App Store could do this, adding games could help with casual gaming. I'm not saying it will replace the XBox or PS4 for proper console gaming, but what about games such as Angry Birds? And with this rumour (if it's true) about the motion sensitive remote it could be really good. obviously this is going to depend on games and as you say some games won't work, but others might, people might be more willing to pay £1-£3 for Angry birds on the Apple TV, or racing games that use the remote.
Also as another person has said, Nintendo have confirmed previously that games will be coming to IOS, what if these games make it too the new Apple TV?
I believe Nintendo is not bringing it's classic games though, like Mario Cart, to iOS. But they are making new games featuring their game characters. So what they end up being like who knows? I would also imagine they will launch cross platform, to maximise profit.
But yeah if they actually sell games for a decent price then fair game. I just feel they will still be freemium rubbish. But they could utilise a controller if one is with every Apple TV so it has a potential, potential to offer something.
Don't get me wrong though, I love my Fire TV and use it every single day, I got it for my Birthday after researching, if an up to date Apple TV was out then I would have got one of those instead. These streaming boxes are I think RIDICULOUS value for money.
Steaming is the future of TV, paying hundreds to thousands to watch a few channels is NOT my idea of TV, paying A hundred to watch those few channels IS my idea and I am very glad for these streaming boxes pushing the concept.
Sure you can use a console to stream, but with constant fan noise too.
In fact with the Amazon Fire TV, the Nvidia Android TV and the hopefully new Apple TV, I feel these greedy satellite and cable company's will have a lot to worry about.....
Now if game streaming is offered more and more, than PC and console gaming will ALSO have to start worrying, playing the latest PC games via streaming on your tiny, cheap box. Sounds good to me

And this is a real concept, in America you can stream on the Fire TV using the Gamefly service, and you can stream on the Nvidia TV box using their Grid service. If Apple allows someone to launch a similar service on their device then I think a market will open up even more for streaming games.