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If the code on the game website is available without logging in, then it's a bad idea to base your account creation on the other website on verifying that code...since anyone could find it on the game website (ie: they don't have to login to see it).
You want to do the authentication based on some piece of information that the user gives you, that is only available on the game website to them personally, after they have logged in there.
Then you need to do some kind of web services call to the game website to verify this information against the game website's database.
Since you're looking for a way to authenticate individual users, Registration Codes is not useful in this case.
But it does sound like the exact situation openID is meant to handle. If you enable both sites to use openID, then basically people should be able to login to your website using the same login they use on the game website.
Good luck,
--Julian