Oh, that's the file extension for files that are meant to be downloaded by the Amazon music downloader. Unfortunately, Amazon doesn't have a 64-bit downloader for linux.
Help comes from Pymazon (http://code.google.com/p/pymazon/). I installed pymazon (using the
current mercurial branch), and "pymazon -c AmazonMP3-1295025407.amz" was enough to download the file. It even made it through the corporate firewall. Cool!