Google Play Movies and TV support is starting to roll out to Google Home speakers, though it is worth noting that it seems to be available for some users but not all, as attempts to get content to play from the Play Movies library yielded no results. Also worth mentioning is that the attempts were made using the Google Home Mini as well as the Google Assistant-powered Sony smart speaker. You will need to have a Chromecast plugged into a TV or monitor, have a device like an Android TV box plugged into a TV or monitor, or have a TV or monitor with Chromecast technology built-in and have them powered on for Google Home to initiate the playback, so that's something to keep in mind.
Google's support page now lists Google Play Movies and TV as a supported service which Google Home can play content from, so the feature has definitely been enabled though it might take a little while before it actually activates for everyone and there's no way to tell how long that might take, so if you have the necessary equipment and you're interested in using this feature, you'll just need to keep trying to use it until it works. That said, it's also specifically noted that Google Home can initiate playback of movies and TV content on a TV with Chromecast plugged in or built-in, so this probably won't initiate playback on the screen of your phone or tablet.
If you already have a Google Home or Google Assistant-enabled speaker setup then you won't need to link your Google Play Movies and TV app to the Home app as Google notes this is automatically done, so really all there is to do is wait for the feature to work if it isn't already. One last thing to keep in mind is that while Google's support page only mentions Google Home, this should also work with the Google Home Mini and Max as well as any smart speaker that's powered by Google Assistant.