No audio on Xbox at all through headsets

Does it at least support game audio through the included Xbox One headset?

n4g.com/.../microsofts-albert-penello-confirmed-xbox-one-supports-game-audio-through-headset

When you plug a headset into a controller, the game audio and any chat you do is automatically goes through the headset speakers. Check the audio settings on the guide to make sure they are not low. press the Xbox button on the controller, move all the
way to cog icon, and select the audio option, from there you should be able to see the volume and mixer options for the headset.

From the PS4 FAQ:

Will the DUALSHOCK 4 controller’s 3.5mm headset jack support other headsets or headphones?

The PS Vita system’s headset is fully supported. Some other third-party headsets may support basic audio and chat functionality on PS4, but Sony Computer Entertainment cannot guarantee it.

Is it possible to output all game audio through DUALSHOCK 4 controller’s 3.5mm headset jack?

Yes, you can select the Output to Headsets option to either ‘Chat Audio’ or “All Audio.”

The chat headset is designed to only give you chat audio, and leave game audio coming through your television.

Any other headset will give you both game and chat audio through the headset, whether you use the new controller or the older version with the headset adapter.

I'm talking about plugging in any stereo headset (like earplugs) to listen to all game audio instead of outputting it through your TV. The Wii U does this with their GamePad (you can play in off TV mode and listen to the audio). The sound quality is awesome.
I've heard the PS4 will let you plug in a stereo headset and output all game audio (sounds, music) to the headset in 2.1 sound. Will the Xbox One allow the same thing?