I have 2 devices. On one device I can see 2 buttons to register/login as facebook or google play games. On the other device I can't see these buttons. All the rest is there, only the register buttons are missing.
Most likely it's because you don't have updated either Google Play Services or the game itself. You can update Services through Google Play.
I just had this problem on a device that used to be mine, that I was setting up with a different profile for my daughter. It wouldn't give me connection options. I uninstalled and put her in as an 18 year old, and then it gave the social media options.
TL;DR: maybe it's set to too young an age