It looks fine to me in Firefox, but iNaturalist doesn’t officially support animated GIFs, so I don’t think they’re not working would be considered a bug.
that said, gif animation is not really intended to be supported in the system. so i think any solution here will probably need to come from the observer, who could try just reloading the image file, if the current uploaded images are problematic to them.
for my own videos, i upload actual videos to YouTube and then link to that in my observations. if you’re already loading things to Wiki Commons, then presumably you could link to videos there.