In my experience, if I started a game - any Big Fish game - using the shortcut Big Fish creates, the Game Manager never completely closes after exiting the game and blocks me from moving any Big Fish game folder, not just the game I was just playing.
If you try to move or manually delete a game folder while the Game Manager is running, you'll get a 'file or folder in use' type problem. There are other ways to uninstall where there is a 'file or folder in use' problem if the Game Manager is running. If you uninstall through the Game Manager there shouldn't be a problem.