^Sure you can do that. But the quality is crap and you have to listen to each and every song in its entirety and mess with that recording program. I did it the easiest way possible with the best possible end result. This is exactly what you do to manually download the files on this site:
Start a song. When it's playing, hit CTRL + U to view the source of the page. Then take the PHP document name found under the Javascript that plays the music file and paste it into the address bar in the same root subdomain. Then it will open the unique PHP document. Do CTRL + U again and it will give you the exact URL to the MP3 file. The URL is located in the PHP code, but it's easy to see because it has a .MP3 extension. Alternatively the unique PHP document has the direct URL to the MP3 file, but it has a space and extra "/" in it to prevent automated downloads. Just remove the space and slash and copy and paste the URL into a new browser tab/window. Then it will ask you if you want to download it.