Google Play Game Services provides more features for game developers than achievements and leaderboards. None of them really fit the game we are building, but it is useful to know they exist just in case your game needs them. You can save yourself lots of time and effort by using them and not reinventing the wheel.
The other features of Google Play Games Services are:
Events and quests: these allow you to monitor game usage and progression. Also, they add the possibility of creating time-limited events with rewards for the players.
Gifts: as simple as it sounds, you can send a gift to other players or request one to be sent to you. Yes, this is seen in the very mechanical Facebook games popularized a while ago.
Saved games: the standard concept of a saved game. If your game has progression or can unlock content based on user actions, you may want to use this feature. Since it is saved in the cloud, saved games can be accessed across multiple devices.
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