I have in the past downloaded and installed free games from the "Game Giveaway of the Day" site, but the past two times I tried, I get up to the point where one of the items downloaded is "Setup.gcd" and I'm told Windows doesn't know how to open this.
I have no idea what this setup file is and I am stopped from continuing the installation since this "gcd" information is necessary to play the game.
I'm running Win7 64-bit.

Is there a way around this?

Mary, you should have 3 files in the extracted folder... Readme, Setup and setup.gcd. You don't open up the setup.gcd file. Ignore it. The only file you click on to install is the plain Setup file with the "key" icon. I'm not sure what it all means, but the .gcd file is part of their "wrapper" and is necessary for correct installation. If you read the readme file, it explains it all.

I get a message that I've successfully activated my game; problem is, I can't find any evidence of it ANYWHERE! Even if I do a search in files and programs, all I can find is the WinRAR file that I downloaded the Setup.exe from.
How can I have activated a game that's not on my computer?
I'm totally confused.

That's because this game is installed in your Games folder and it doesn't put an icon on your desktop. The path for the folder is also given in the Readme file. This is a copy and paste from the Readme file...

path by default - C:\Games\Game_AlabamaSmithEP

I changed the path when I installed it--but I finally found the game! I wonder why a search didn't find it? Even looking in the program listing in the "uninstall" program in the Control Panel didn't show the game as installed.

But anyhow, all's well now. Thanks!

It isn't in my Control Panel listing either, but I find that a lot of these Alawar games aren't. Have fun - this is not a bad little game for a freebie.