Are there any warning messages in the graphics section on the "Help > Troubleshooting Information page"?

You can also check media prefs (search media.*enabled) on the about:config page. You can open the about:config page via the location/address bar. You can accept the warning and click "I'll be careful" to continue.

• http://kb.mozillazine.org/about:config

No warning messages on that page, though 'hardware H264 decoding' reports 'false' (if that is anyhow relevant).

The only settings modified in about:config page are:

• media.gmp-gmpopenh264.enabled
• media.mediasource.webm.enabled
• media.peerconnection.video.h264_enabled

I've tried resetting them to default settings and also enabling the options that are disabled by default but to no avail.

The playback worked fine before, the only thing that has changed was the mentioned windows update.

I have installed a fresh copy of Firefox Developer Edition to have a fresh&clean environment and H.264 didn't work there either, so the issue is somehow related to what has changed in the newest build of Windows and not to Firefox itself.

If I'll manage to find a fix for that I'll report back with the solution.

I have found the source of the problem and a solution.

The real problem was that my version of Windows was a N one (without media features, including codecs) and updating it to version 1511 (build 10586) silently removed/disabled a previously installed Media Feature Pack and reinstalling the old update file is not reenabling it.

Solution: install KB3099229, the new 'release' of Media Feature Pack.

Another thing is that Firefox silently depends on the MFP without notifying user that it might be missing...