Here was the response I received from Stardock:
"It sounds like the archive is corrupt. There is a way to trick Impulse into to getting everything installed, though you will need to download some, though not the entire game. Navigate to the install directory for the game. Create a blank text file, and rename it to 'GalCivII.exe'. You'll need to have file extensions showing in order to do this. Then go into Impulse, and click the menu button (blue, upper left), then select 'Detect Application'. Point to the install directory, and Impulse should then recognize that it is installed. Then hold down the 'shift' key, and right click on the entry in Impulse, and select 'Verify Installation'. After a bit, it should prompt you for an update. Once the update is complete, you should be able to run the game."
At the time I sent this I thought I was only missing the game executable, however, I am also missing all the game files. The above will download the ENTIRE game again. I sent an email back pointing to this thread. The problem is that now, I can't even unarchive the games anymore because I am receiving a different error from trying to uninstall the empty directories created by the first time I tried. However, I can still download the games if I want.
I have uninstalled impulse and moved on to other things. I am glad I only bought a couple of games from Impulse. Crap like this is why I don't use Steam, Direct2Drive, and now Impulse. I thought I would leave this message since the above poster wanted the response.