The current Games tab on the pager is flunky. It is more like a list of active servers, and more specifically of active servers of your favorite games. This is perfectly fine, but the tab should be labeled more appropriately.
A proper Games tab should be more like what 'My Hub > Games' from the file menu displays: A list of all games that you currently have downloaded to your computer. From this tab, you could easily delete or launch games, and server listings could be provided here as well.
* Steam provides an excellent example for game distribution mediums.