Facebook's Android TV app is live on the Play Store now but it only plays videos, and doesn't let you access any of the other stuff you'll find in the standard app that you can access on your smartphone or tablet or through the desktop website. The purpose of the app seems to be purely for letting users access their videos with a simpler interface that isn't bogged down with all kinds of other content, such as news stories, regular posts from friends and family, images, games, and anything else that Facebook generally offers on its other supported platforms.
While this might seem like an odd move, it might not if you consider that Facebook is taking an approach that seeks to focus on the kind of content that will look best on the big screen, such as videos. There are multiple tabs for video types if you want to filter down what it is that you're looking for to watch. Of course this will include suggested videos that Facebook thinks you'll like and which may be based on other videos which you've either liked in the past or commented on or shared. If you've interacted with it in some way, then it could factor into what videos are suggested.
Other categories include your personal videos, as well as a search option which does just as it says – lets you search for videos. The most pinpointed method for finding what you want might be to search for a video, at least for now, though Facebook may update the app in the future to have more video categories. In fact, Facebook is reportedly preparing to add in a category for videos based on games and eSports content on June 10th, which means if you enjoy watching gaming-related videos then it won't be more than a few days and the app should include this new category. That said, even if Facebook launches this new game video category on June 10th as planned, it may take a few days to roll out to all users. If you've got an Android TV device of some kind, you should be able to open up the Play Store app and search for Facebook and the app should pop right up.