If you can’t get enough of the videos you find on your Facebook News Feed, the Facebook Video app for Android TV was made for you.
Available inside of Google Play from within the regular Facebook app (just search for Facebook on the Android TV), the app’s sole purpose is to display different video categories, then play the videos you want to see. As for the categories available, there is Suggested, Live, Topics, Games, Your Videos, and Search.
As for the devices that are supported, it appears any Android TV device can run it. That includes Nexus Player, SHIELD TV, etc.
Have at it.