If I paste the following URL directly into the address bar in Firefox, the video plays just fine:
http://distilleryvesper1-13.ak.instagram.com/744b42900fab11e3a34522
You are probably on Mac and you have the QuickTime plug-in installed, so the plug-in plays the video if you navigate directly to it, but it doesn't work in the video element, because Mac support for MP4/H.264/AAC isn't ready yet.
As of November 2013 / Firefox 26, Firefox supports MP4/H.264/AAC on Vista and newer Windows, Android and Firefox OS.
Your Fiddle also works on Linux when GStreamer support is enabled and encumbered codecs are installed. (GStreamer support is not yet enabled by default in e.g. builds supplied by Canonical for Ubuntu.)