Whether you're relaxing at the beach or taking a road trip, Google Play Music delivers personalized music based on where you are and why you are listening. This means that Google Home will play the special, extended version of a song that you've either bought or purchased and not the bog-standard version that the radio plays. But while you could indeed stream from Google Play Music to your smart speaker, you were only limited to what's on their online catalog. To do so, ask "Play [x] from my library" or "Play my [x] playlist".
You can not specify the song location when asking Google Home to play a track by genre or mood.
But if you ask Google Play Music to play a genre or music from a particular mood or activity, it will still prioritize the online catalog of course. But as part of a server-side update, uploaded and purchased songs can now be requested and played. The feature is now rolling out across regions around the globe and should soon be live in the countries, where Google Home is supported.