How to determine what kind of Safari plug-in for streaming video is missing?
If you click on the "Missing Plug-in" message in the Safari window it should display a pop-up message that says. This is telling you that you need a plugin that allows you to view WMP (or Windows Media Player) content.


  This page contains content of “application/x-ms-wmp” type. You do not
  have the plug-in required to view this content. This page may have the
  plug-in for you to download and install:
  
  http://www.microsoft.com/Windows/Downloads/Contents/Products/MediaPlayer/
  
  Do you want to open the page?
  
  [Cancel] [OK]


If you click on OK it will then attempt to load that page which, after being redirected a few times, should lead you to http://windows.microsoft.com/en-us/windows/personalize-windows-media-player. Unfortunately this page is not very helpful but there is a link to "Get other versions".

If you click on "Get other versions" it takes you to http://windows.microsoft.com/en-us/windows/download-windows-media-player which near the very bottom, beside "Mac OS X" has a big purple "Get it now" button.

If you click "Get it now" you are taken to http://www.telestream.net/flip4mac/overview.htm which offers the Flip4Mac plugin as mentioned by Tetsujin in the comment above. Previously Microsoft used to subsidise/sponsor/pay Telestream to distribute Flip4Mac for free but stopped as of May 2004. In theory if you are just wanting to play WMV videos (like the one on that site you linked above) then the 5.95 USD Flip4Mac Player should be enough.

However in my own testing if you purchase and install the Flip4Mac plugin within Safari it still does not work with this site. You just get an error "The operation couldn't be completed. The file is not a movie file. (-2048)" I don't think this is a problem with the plugin necessarily because it works fine on other sites. It just doesn't work for me on this particular site.

I get the same error in Chrome. Even after enabling the soon to be removed NPAPI plugin support that is required for this type of plugin as described here https://support.google.com/chrome/answer/6213033.

So that is how you determine which plugin is required to play video on that site. Sorry I didn't have a more positive answer for you. Hope this helps in some way.