Some paid games use drm which needs gplay services to function.

MicroG is what probably is making it work for you. However not everyone uses microG.

Check out Mull or Mulch. Mull is a more private Firefox and Mulch is a more private Chrome. They are made by the DivestOS team, they also make DivestOS which is a lot more private Android version that supports a huge number of phones. That’s how I’m also runing the latest version of Android 13 with the latest security updates on a phone from 2019. And there are much older devices supported.