Isn't that what CSRF protections are for, not CORS? There are other (very old) ways to trick a user into doing a POST that wouldn't be blocked by CORS -- and as you say, GET and some POST requests can always be sent but you don't see the response.
My understanding is that the actual protection that it gives in this scenario is that the "fungame.com" JavaScript cannot read your friends list or your list of private messages (basically, blocking GET data that should not be shared to random sites, as it would violate user privacy). You still need CSRF protections regardless of CORS.