Ah Gizmodo, always the paragon of good journalism. The person has explicitly asked her tweets not be used in external websites, and of course this zombie tabloid doesn't give a damn
If they cared, they wouldn’t post publicly or the service would not allow that message to embedded.
An enforceable request is called a “demand”, and unless you’re actually capable of enforcing it, it is in fact still just a request.
It would have been polite to honor the request, but they are under no obligation to do so.
Don’t make public posts if you don’t want them publicly displayed.