It's really more of a browser issue, a GIF you can just right click and download, but they don't make that option available for videos.
That option does actually exist for "plain" HTML5 <video> tags, as far as I know. It's just that most videos aren't hosted as simple as that, and are effectively stitched together out of multiple MPEG-DASH, HLS etc. fragments – or the site uses a custom video player.
In both cases, the result is a lack of a right-click-to-save option.
<img src="v.mp4"> is a thing, but unfortunately it’s not supported outside Safari. https://stackoverflow.com/questions/60114243/using-videos-in...
The contract for these could be something like "no sound, default playback in a loop, 30 seconds or less; don't render if any of these requirements aren't met" to make sure people don't abuse it for auto-playing videos.