The Games are just hosted on Google+ / Facebook, and the game progress is saved in the servers of the Game Developers (Eg.: Zynga, Digital Chocolate, Wooga). You cannot delete your Game progress as such.
Even if you revoke the access of the Game from Google+/Facebook, the progress will not be deleted and you will be able to continue playing the game from the same point by opening the game again and granting the game access to your account information once again.
Deactivating Facebook account also does not helps.
In Google+, even if you delete your complete Google+ Profile, your progress does not goes away. You can always recreate the Google+ account with the same GMail address and continue playing from the same point.
Deleting the whole Facebook account (after waiting for the 15 Days "Deactivation" Period) and deleting your whole Google Account (with GMail Address, Contacts, Docs, Calenders everything gone), can alone prevent you from continuing your game again.
Even then, your game progress will be available in the servers of the company, it will just become in-assessible to you for the rest of your life.
Best Answer
No, that is not possible as of now. Because games are associated with your Facebook account. You can use Messenger without having an active Facebook account just to have conversation with your contacts but you cannot use any other service of Facebook by just login to Messenger.
You will not be able to access Gameroom if you deactivate your account.