I don't think the current popularity of GIF compared to HTML5 <video> is really because of autoplay (since <video> can do that too, and loop too).

The big advantage of GIF is that it works in an <img> tag just like any other image, so you don't need a website to explicitly support it.

Another advantage, I think, is that GIFs are guaranteed not to play sound, which is great when browsing say imgur.com or pr0gramm.com at work (edit: of well, I had missed the "muting me" part of your comment, so let's just say that we agree that it's an important component).