It doesn't break any law of physics and that's not what's claimed in the video. The thought experiment is simply to demonstrate paradoxes in the classical notion of identity. The solution to this supposed conundrum is actually pretty simple; there isn't any essential "you" who has experiences. There's only experience itself, i.e. experience is the net result of being, not a thing that beings do. At the moment that two exact copies emerge from the transporter they cease to be exact copies, simply by virtue of the fact that they no longer occupy the same space. They're both equally "you" inasfar as a "you" exists, which is to say that it really doesn't, at least not in the sense of an essential being. The continual chain of cause and effect that thinks of itself as you is multiplied and split so that each chain is now separate, operating from two different perspectives at once. That situation is not essentially different than the situation of your experience existing alongside the experience of a person who's been separate from you their entire life, i.e. just another person.