Possible to switch between Google Play accounts?

Okay, so it looks like none of the apps on my son's phone are connected to his Google Play account.

I changed the setting to automatically sign into any apps with Google sign in but it doesn't seem to have made any difference.

What I am saying is that I believe his game account is just on his phone and so I can't sign out of it to sign in ton my shardmates account if that makes sense.