SgtSurehand I downloaded Google Play Games and the game in question from the Play Store. The game wasn't connecting to my Google games account so I tried uninstalling it and downloading it through the Play Games app. (Long shot, I know.) It didn't solve the issue but did at least show that those two Google apps were communicating with each other. I've tried downloading the game through those two apps and Aurora. It doesn't recognize Google through any of those methods.
I also tried installing Shelter and doing the same process over there. Didn't work. I have Google Services installed on my Owner profile, including the Play Store, just not logged in, hoping that would help but still no luck.