It appears that on upload, Twitter is converting the GIF to an MP4 and embedding the video instead. Why would they do such a crazy thing? Well, size and control.
GIFs are terrible at compression. The original GIF above is 500kb while the mp4 version is only 100kb. A GIF is literally a sequence of independent images squeezed into the same file. An mp4 video can take advantage of all kinds of fancy compression techniques like keyframes and forward-predictive frames.
If most of your users are on mobile, this is a huge win. Even desktop users will notice better performance on a page with many GIFs.