I can't get this video to play in FIrefox 37.0

When I click to play the video on this page, it replaces the picture with text saying

Requested Format Not Available

None of the requested formats are available for this content

YouTube works just fine and some other videos, but some sites baulk. This page marks the video as type="application/x-shockwave-flash".

I'm running Firefox 37.0 on Fedora 20. I do NOT have any Adobe plugin installed, that is, my /usr/lib64/mozilla/plugins directory is empty. But when I go to Add-ons and search for "flash", I see there are 664 results. I've tried about 4 of them.

Can anyone play this without the Adobe plugin installed? How?

BTW, Chromium 40.0 does exactly the same thing, though I haven't experimented with it as much.