For whatever reason I can't play anything on this web-site.

Most probably the web-site uses RTMP or HTTP flash video streams. Try to record them with Replay Media Catcher

For more software please go to our FAQ:
FAQ: How to record/download/capture/save Adobe Flash .FLV video RTMP stream from embedded player
FAQ: How to record/download/capture/save Adobe Flash .FLV video HTTP stream from embedded player