Pangea Software founder Brian Greenstone has published a developer tutorial for adding 3DTV support—that is support for television sets with 3D—to their Apple TV 4th Generation games. This is trickier than it might seem at first blush because neither tvOS nor Apple TV support 3D TV—but Mr. Greenstone has figured out how to do with through tools available in OpenGL, and he's sharing.
Pangea Software is one of the oldest Mac developers on the planet, and the company was among the first to embrace iOS when Apple opened the mobile platform up to developers. When the new Apple TV App Store launched, Pangea had five games ready to go, and all of them supported 3DTV: Air Wings, Bugdom 2, Nanosaur 2, Nucleus, and Otto Matic.
If you've downloaded them on iPhone or iPad, you can find them on your Apple TV App Store under Purchased—otherwise search for them on the Apple TV App Store).
From the tutorial's intro:
The Apple TV and tvOS do not inherently support 3DTV in that there are no tvOS APIs for such a thing, and the Apple TV cannot send an HDMI signal to the TV to tell it when to switch to 3D or 2D like most movies do.
Regardless, adding 3DTV support really is quite simple with any OpenGL application, and most modern 3D-capable TVs will auto-detect when the Apple TV is showing 3D content and when it is not.
The short version is that he's providing a left eye and right eye image in a way that your 3D television set can use it to generate a 3D image. For Bugdom 2, it looks like this:
Image from Pangea Software
The full tutorial at Pangea's site has code and instructions for the whole shebang. Good luck!