How to diagnose plug-in failure with flash 13.mumble and Safari 7.0.3 on Mavericks?

I recently accepted a flash update, which if Installed Plug-Ins is correct has me at Shockwave Flash 13.0 r0 for my 7.0.3 Safari (9537.75.14) on 10.9.2 running on my mid-2007 24" Intel Core Duo iMac. Alas, when I go to a site such as http://www.theatlantic.com/technology/archive/2014/04/flyndrive-notes-from-all-o ver/360495/ , where the video should be playable I get "Plug-in Failure." How can I go about finding-out just why the plu