There's nothing about allowing play/pause that prevents videos from behaving exactly like gifs. I've seen browsers with play/pause options for gifs, even.
The stop button used to stop all gifs on a page in firefox and internet explorer. Not sure if that was a bug or a feature though, since the stop button was generally not available when page load finished.
(Maybe I remembered wrong, someone else mentioned here that it was ESC, not stop)
At least on Firefox, it was indeed stop. I believe it still works too, even though nowadays they hide the button, if you expose the functionality through an addon.
Can you tell me of one, please? I'd like to check their implementation, most play/pausable gifs I see are only converted webms.