I've worked with a couple web designers and developers that said "Gif" to mean any image, as in "Move that gif up twenty pixels" when referring to a logo that's actually JPEG. I think it's a holdover from the days of BBSes and AOL and CompuServe, where everything really was a GIF. "Check out this new cheerleader Gif I got." It's not a far leap to imagine these users just out of habit and familiarity clicking GIF in the save-as dialog without really thinking about it. So GIF persists out of familiarity and inertia.
There are a lot of cases where PNGs are superior, mostly because of the extra color depth. But that's not enough for a speedy transition.
I'm not sure off the top of my head what HTML 5 market share is like (anyone with recent data want to chime in?), but I'm guessing lots of people are running browsers that still don't have <video> capability.
The percentage of users not able to use <video> is roughly equivalent to the percentage of users running IE8, which is about 20% right now, and probably will stay there in the near future, as XP users cannot upgrade to IE9 (thanks, MS!).
The other problem with <video> is that there is still no common format which every browser supports, so even if you would ignore IE8 (or provide a fallback via Flash) you'd still have to encode all videos twice (to H.264 and WebM/VP8).
Sad as it is, but Flash for video and animated GIF will stay with us for some years.
I wouldn't be surprised if those short videos were the bulk of the GIFs around. At least of the GIFs actually used and being dormant in some long forgotten archives.