You can remove (or manage) links in the Games menu through the registry. The key for this can be found at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\GameUX\Games.

For each entry there's a subkey named a CLSID. When browsing through the list, opening a CLSID reveals the actual title, path and some other settings of that entry. If you want to remove an entry, find the right entry by checking titles and/or paths, then delete that key.