This seriously is a huge item being neglected by Twitch here. People expect this from installers. I (unfortunately) have a half dozen of the darn things now, and Twitch is the only one I can't choose whatever folder I want. And not being able to migrate the files for a game from one location to another is frustrating too.
Edit: It's great that someone apparently found a workaround, but having to install database management/editing software and learn how to do everything that comes with it and risk borking your system is asinine when it could be so easily implemented by Twitch.