It simply pulls the file up in an in-browser streaming thing. I want to download the actual MP3 file to put it on my Android for a 3hr drive I am about to do.
Most browsers will do that with audio and video files. You have to right click on the link and select Save As.
Assuming GiantBomb actually wants that button to download the file, they should be returning "Content-Disposition: attachment" as one of the HTTP response headers (I checked with curl and it's not sending that currently). That should prompt the user to download the file on all browsers.
Here's a link to some MS documentation about it: http://support.microsoft.com/kb/260519
I posted a thread in Bug Reporting about this, which will hopefully be seen by the appropriate people: http://www.giantbomb.com/forums/bug-reporting/33/bombcast-download-mp3-button-opens-the-mp3-in-the-browser/553932/