If I paste the following URL into Facebook I can share an animated gif. It\'s not a movie and not flash, Facebook now supports gifs without those workarounds. I can click it
Actually, I looked at their source code, and I am 99% sure that they are actually showing a video. For this gif, there are a number of open graph meta tags associated with the page:
and most of them are video tags. These tags are associated with the page and not a gif. If you share the straight gif image, then it will not animate.
To confirm this, if you plug the page into the Facebook URL debugger, then this can be confirmed. There is no mystery, this is shared as a flash video.