Facebook does actually allow you to prevent notifications from users, groups, or games. Please follow the directions here: 

https://www.facebook.com/help/messenger-app/276605209445733

Though the above directions were written with group chats in mind, you can also block notifications from games, apps, and individual users using the same process. Please note that this will only prevent notifications - the messages themselves will still be sent to you.

Thanks for playing!