I can't save this flash .flv streaming video for you.

I've used freeware URL Snooper to find the URL and it showed me simple http:// .flv video.

There are lots of ways to save such videos:
How to record/download/capture/save Macromedia/Adobe Flash .FLV video HTTP stream from embedded player

The problem is that the URL seems to expire very quickly so I can't save it with a download manager.

I've also tried WM Recorder and Replay Media Catcher, but for whatever reason they were not able to find the stream URL automatically.

And the video is not saved in the cache of my browser.

ATM I can only suggest you to use screen video capture software to record the video from your screen.