Is it supposed to? I just took a look at the site and it only appears to want to stream audio to you. All the samples play nicely but picking "New Releases" and then the "Stream All Songs" brings up the dialog box "Launching Download.com Music Player"
To see anything happen, you have to turn OFF any Pop-Up blocker you have running. Go to the menubar, Safari/Block Pop-up Windows and the check mark will be removed. See what happens then.

I never did find a place to actually download these tracks.

P