You don’t have to use the same image for the feature as the embed preview. The featured image is often the default (and you have a fallback just in case), but you can also choose to replace it for socials. Don’t know what this is built in (on mobile) but it could just be using a different file.
I haven’t seen this before so grain of salt but I’m assuming it’s just to be eye-catching so you click to their site. I’m also assuming you wouldn’t want it to be a gif on your own site because of accessibility concerns, but that depends on your requirements which vary pretty widely by country.