Regardless of the legality of the action or the product itself, a video reviewing, showing or reporting on it shouldn’t be passable of a copyright claim.

Even if the video shows copyrighted material, it still shouldn’t be allowed for Nintendo to claim it, as that would fall under fair use. Just showing a few screenshots of a video game for the purposes of education in an otherwise unrelated video would never fall under copyright infringement.

The piracy argument has nothing to do with Nintendo claiming a video as their own, despite them having no rights to do so.