Firefox uses gstreamer-0_10 to display HTML5-Videos.
So make sure that you have the necessary gstreamer-0_10-plugins packages installed (from Packman).
In particular:
gstreamer-0_10-plugins-bad
gstreamer-0_10-plugins-bad-orig-addon
gstreamer-0_10-plugins-base
gstreamer-0_10-plugins-ffmpeg
gstreamer-0_10-plugins-good
gstreamer-0_10-plugins-ugly
gstreamer-0_10-plugins-ugly-orig-addon
It depends on the particular video of course, which package is needed exactly.
If you have all those that are listed, you should be able to play (nearly?) all videos.
The videos from your site play fine here with Firefox 29.0.1 btw.
As they are .ogv only the package gstreamer-0_10-plugins-base should be needed, but better install all of them, I’d say.
Yeah, right.
And then there’s also gstreamer-0_10 vs. gstreamer-1.0.
Well, at least the latter “problem” should be solved in 13.2. AFAIK most of the stuff has finally been ported to gstreamer-1.0 by now, including Firefox and phonon-backend-gstreamer.