I'm really not seeing what problems this would fix, and it would certainly cause me some minor ones.
This would break my workflow. I often keep chat on one screen while I'm at work. I'll occasionally glance at it to follow the conversations. Forcing me to move my mouse all the way to the chat window and click just to play a GIF is a rather big waste of time. I'd probably still do it, but you've just wasted 10 seconds of my time moving my mouse.
Moreover, the click-to-start, click-to-stop behavior breaks the existing functionality where I can click on an image and see the original at full …