I have a large library of content in Google Play Movies & TV and it doesn't show up under the "library" tab on Google TV. Even when I search for a movie that I own inside Google's infrastructure it doesn't give me an option to watch via Google Play. Instead it tries to get me to pay for some other service to watch it (Hulu, HBO, etc). If I manually go to all apps and open the Google Play Movies and TV app all my content is there. Basically there is no way to find or play my owned content via the normal Google TV interface. It is only accessible if I manually launch the old Google Play Movie & TV app.
This is super frustrating as this is one of the main reasons I wanted this Google device is to watch the large library of content I have paid Google for.
Don't forget you can see your library inside of the YouTube app.