The Google Play Movies & TV app for iOS has received an update today, which is already live in the iTunes App Store. The new version finally brings with it support for playback on Apple TV, through AirPlay - nicely complementing the already built-in Chromecast functionality.
There is a caveat unfortunately. For this to work, you need to have the 3rd generation Apple TV or this year's 4th gen model, and it has to be on software version 7.0 or higher. If those two requirements are met, then you can finally use your Apple TV to watch the movies and TV shows you've bought from Google's service.
The newest iteration of Play Movies & TV also supports HD streaming (better late than never, we assume) as well as streaming over cellular network connections. To top things off, the app has been redesigned, and it features new recommendations.