Here's a few threads describing the problem on several devices, including televisions and the Nexus Player. Some people even say it affects the Nexus 6p smartphone as well.
https://productforums.google.com/forum/#!topic/nexus/B9w14NuBv5U
http://forum.xda-developers.com/nexus-player/help/brightness-playing-videos-marshmallow-t3220531
Does anybody see this issue? It doesn't affect Kodi v15 since Kodi has its own display implementation so you can only see the issue on apps like Youtube which run Hardware-Accelerated all the time or by default.
The only workaround is turning hardware-acceleration off in your player, which can be done in MX Player or the Archos Player but not Youtube.
If you see the problem on your device, let Google know to fix it when they roll out 6.0.1!
Edit: here's the only bug report on the Android issue tracker I could find. Let's star it and other issues to give it more attention
https://code.google.com/p/android/issues/detail?id=188667
EDIT: 11/10 - The aforementioned bug has just been marked as assigned
From day 1 I haven't liked the image on my Shield TV and stick to my older HTPC for Kodi to playback local NAS content. Everything looks washed out on the Shield, terrible blacks etc. Thing is I'm not on Android 6 yet, and I noticed this when I got the Shield back in July.