Android TV apps vary greatly in terms of functionality. Some are close to what you get on a phone, but others are focused on a single experience. Case in point, the Twitter app for Android TV that only shows you videos. The new Facebook app is similar—this app simply makes it easier to access the videos in your feed.
Facebook for Android TV is available at the same Play Store listing as the regular app. You can search on the Android TV Play Store or push it from the web. To log in, you'll need a web browser to open the device authentication page. Enter the code shown to associate the Android TV app with your account. It only takes a minute to get all this set up, but casting from your phone actually seems more convenient to me.
The app has categories for suggested videos, your videos, and search. You can watch, bookmark, and like videos from the Android TV app, too. The SHIELD controller also zooms the video when you press the trigger buttons, but that might be an unintentional bug as it seems pretty useless.
If you want to sideload the Android TV app directly, we've got it on APK Mirror.