I can't tell if there is any widespread problem with the Big Fish Game Manager.
At the moment it's working as it usually does on my computer and I purchased and installed some games earlier today.
You should be able to play games that are already installed and activated by starting them directly from the game's exe without going through the Manager or the desktop shortcut created by the installation.
For new games or games that have been uninstalled, you'll have to get in touch with Big Fish customer support.
It's possible that your antivirus is blocking some aspect of the Game Manager. I noticed Microsoft Security Essentials wanted me to submit a DRM-related file from several newer Big Fish games, and a different antivirus might simply delete the file.