Good lord, Twitter doesn't make it easy to rip their video clips.
If you dig through the source, you'll find a link to an M3U8 file, which contains a link to more M3U8 files, which contain links to a series of TS files, and if you give one of the M3U8 files to ffmpeg, it'll download the H.264 video for you.
I have an iOS shortcut for ripping YouTube clips to your photo album. I'm not sure if one could be made to download these M3U8 files, though...