As to the Xbox question. The HDMI output setting of TV and PC sets the black and white points. TV is 16, 235 with full head and to room preserved. PC is 0, 255. In this case video will be expanded from 16, 235 to 0, 255 and everything below 16 and above 235 in the original signal will be clipped. On the 360 this was called Standard and Expanded.
Most HDMI devices have this option. I don't like the names limited and expanded as it sounds like you are losing out on video when using limited. The names were taken from the HDMI spec. I am trying to get the names changed on the Xbox One.
As to games, that is dependent on the game. For games that are developed 0, 255, then TV will remap them to 16, 235. There is an API for the game developer so they can specify if they developed the game for 16, 235 or 0, 255. Most games are 0, 255 at this point. There was an issue with Killer Instinct where they implemented this in reverse and you can imagine it was busted.
They issued a tile update a while back and it should work correctly. There are other games that have not done this yet. They need to do it.
If you wanted the best of both worlds, you would use TV for video content and PC for games. This would require two different display settings so brightness and contrast would be correct for both. This would mean you would have to switch between the two outputs as you switched between video content and games. The problem gets worse when you have video inside of a game.
I know there is some confusion on boards where people have some displays that claim they support RGB Full and so they switch the Xbox One to PC (Full range) and they are mad because things don't look correct.
This is not a new problem. Computers have always been 0, 255 while video has always been 16, 235. This was always a challenge on Windows and there is no perfect solution today. If you watch content in WMP or Xbox Video, you would get 16, 235 converted into 0, 255. If you used Media Center, it would behave like a CE device and video would be 16, 235. Every time I say 16, 235, assume I mean 1-254 is intact with black and white points being 16, 235. If you use the QT player on Windows, it also plays back at 16, 235. This is why the same MP4 will look washed out in QT player and not in WMP.
I hope all of this makes sense.
If not, let me know and I will try and clarify. Typing this on a Surface Pro 3, so please excuse any typos as I am still getting comfortable with the keyboard.