This autoplay and auto download issue also affects the portable version of Telegram, which is the one I prefer to use. This can become a bit of a chore, especially if your friends or groups share a lot of media. Now you will have to click on each photo to fetch the media. This problem isn't limited to GIFs and videos, it also extends to the automatic downloading of photos.
Note: Animated stickers and emojis are not affected by this bug. You have to click on the media to start the playback, and if you click on a second GIF, the first one stops playing. So every time you send or receive an animated GIF or a video, Telegram just displays a preview of it with a play button on top. The data and storage settings don't seem to affect the behavior either. The autoplay feature does not work in Telegram's desktop app, even if the setting for it is enabled. I wasn't alone, several users have reported that they are facing the same problem. I noticed the issue right after updating the app yesterday. Telegram for desktop does not autoplay GIFs and videos