Moonlight is an open source implementation of NVIDIA's GameStream, as used by the NVIDIA Shield, but built for iOS. Moonlight iOS allows you to stream your full collection of Steam games from your powerful desktop computer to your iOS Device.
Apple TV Note:
We currently cannot port Moonlight to Apple TV due to a limitation in the tvOS SDK that prevents Moonlight from using the APIs that would be necessary for it to work. Thank you for your interest - you can track this issue here.
Check out our wiki.