Tried to download the free games after making an account and I was prompted to use the downloader. So far so good.
Then the diownloader asked me to associate it with a program, so my first inclination was, "Of course, Firefox!" which is my standard browser.
When I try to download the game, a "million" tabs open.

What am I doing wrong?

Have you actually downloaded, unzipped, and run the downloader program itself? http://files.gog.com/downloader/gogdownloader_0901376.zip