Earlier quoted context omitted.
Can you declare a video as looping, and have that correctly honored everywhere it plays? That has always Just Worked with GIFs, but the last time I checked (a couple of years ago) it basically never worked with any “proper” video format.
Yes, just use
That's when you are posting a video on your own website.
If you are posting a gif on a comments section of a website, or uploading to tumblr, for example, you don't have this control