You may use any stream recorder supporting Windows Media streamed through the MMS protocol.

One-click recording of this or other Windows Media streams can be done with WM Recorder.

Or you may record using a regular procedure:
1. Find the URL of the stream.
2. Record it.

To find the URL use Packet Sniffer and URL Snooper software like free Project URL Snooper (some stream recorders like WM Recorder, RM Recorder, Replay A/V, GetAsfStream have a build-in URL finder).

Start searching for the URL (sniffing) with URL Snooper software, play your stream and copy the URL from the list of your URL Snooper software to the clipboard. After that you may stop playing your stream.
Then paste the stream URL into the stream recorder and finally record it.

In this case you may find the URL for the .ASX file in the generated video code:
http://www.videocure.com/music-video...ad25366cc8.asx

.asx file is a metafile that redirects you to an actual stream. Some streaming video recorders can't postprocess metafiles, but you can right click on this URL, click "Save target as..." and save it to the harddisk. After that you may open it with any text editor like Windows Notepad for example and find the following URL
mms://msent.wmod.llnwd.net/a304/o2-orange/msftmsne/Prod/wmv/v9/Video/65/15/54/301541565.wmv

The latter URL can be downloaded using any stream recorder supporting Windows Media streamed through the MMS protocol.