hmmm … do you solve your dilemma yourself, do not you? 
That is indeed possible, immediately start big picture. SteamOS does so ![;)]()
And on Windows that is possible.
But if you’re going to hide it anyway and only use it for gaming, why the extra stop at the Apple TV? Simply work the game tray away in the TV cabinet. No latency anymore, no compression artefacts, if something does not work with streaming, you still have to RDP to that game chip or connect it to a screen. Better support for controllers (I actually have no idea, never tries, but what if I want to connect my T300RS to the Apple TV to stream Project CARS2? Do I have force feedback in that case? Does the rotation of the steering wheel go 1: 1? be taken over? …)
Streaming via the Apple TV is – in the situation that you describe – as far as I’m concerned, hard to do – and then just to do hard, even ….
Psst I was talking about the concept with the L3P D3SK. You do not HAVE to put those lights in naturally. Does not even have to be transparent! I just wanted to show that you do not necessarily have to think of a typical computer case when you say ‘game box’. The CaseMod topic also shows that computer cases are made from a crate of beer ….
The fact that you are quite a fan of Apple (to the Windows bashen) – otherwise do not bother about the stereotypical image of an Apple fan) did me already suspect that the l3p d3sk as it is not your taste. But you can gain inspiration, right?
And on Windows that is possible.But if you’re going to hide it anyway and only use it for gaming, why the extra stop at the Apple TV? Simply work the game tray away in the TV cabinet. No latency anymore, no compression artefacts, if something does not work with streaming, you still have to RDP to that game chip or connect it to a screen. Better support for controllers (I actually have no idea, never tries, but what if I want to connect my T300RS to the Apple TV to stream Project CARS2? Do I have force feedback in that case? Does the rotation of the steering wheel go 1: 1? be taken over? …)
Streaming via the Apple TV is – in the situation that you describe – as far as I’m concerned, hard to do – and then just to do hard, even ….
Psst I was talking about the concept with the L3P D3SK. You do not HAVE to put those lights in naturally. Does not even have to be transparent! I just wanted to show that you do not necessarily have to think of a typical computer case when you say ‘game box’. The CaseMod topic also shows that computer cases are made from a crate of beer ….
The fact that you are quite a fan of Apple (to the Windows bashen) – otherwise do not bother about the stereotypical image of an Apple fan) did me already suspect that the l3p d3sk as it is not your taste. But you can gain inspiration, right?