From what it looks like, if the option "Autoplay GIFs and videos" is off, Riot will serve the thumbnail of a gif instead of the gif itself:
While this is successful if your homeserver has a media repo which does not animated thumbnails, if you do have one that does (such as @turt2live's popular matrix-media-repo) then you will be shown a thumbnail that's still animated.

Logs being sent: no
Animated thumbnails are a non-standard feature. Proper spec is needed in this area.
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Animated thumbnails are a non-standard feature. Proper spec is needed in this area.