It is ambiguous. Sure, if they upload a clip of a movie, that's not ambiguous. But fair use certainly exists, and you certainly have copyright assignment rights

It is ambiguous. Sure, if they upload a clip of a movie, that's not ambiguous. But fair use certainly exists, and you certainly have copyright assignment rights on works that appropriate other works as long as it fits the fair use criteria (or are sufficiently transformative). And you'll still have hordes of unhappy users when you take down their Let's Play videos and videos of their kids when they had Prince playing on their computer in another room of the house.