I used the google demo example TypeANumber from developer.android.com/training. I configured the app correctly in the play.google.com developer console, even published it, confi
I didn't link the game service with the application where the debug key was set. You have to link your service twice with your application, one time your package name with the release key fingerprint and one time your package name with the debug key fingerprint as described in https://developers.google.com/games/services/console/enabling#c_specify_client_id_settings
There is a similar question: Google Play Games - Application in alpha/beta test - Error 10004 at sign-in RESULT APP MISCONFIGURED
Note - if you were developing on one machine and now you switched to a different one, your debug.keystore will be different, therefore you'll require a new linked app since their SHA1 are different.
Not sure if that was your case, but was the reason for my 10004.