There is a setting in Google Play Games that can prevent it from signing in automatically in the game. To fix this, try the following:

• Open the Settings app
• Press Google (Google services)
• Press Settings for Google apps
• Press Play Games
• Press Sign in account (default account for games)
• Scroll down to One Deck Dungeon and check if it shows "Signed out".
• If so, press Change and change it to auto log in.