Most React components won’t have state. That’s the whole point of Redux. There are always edge cases or places where it makes sense, but it’s not the common case (React even supports stateless functions as components since it is such a common case).
And Polymer components can totally have state. So that isn’t really a differentiating factor.
I was unfortunately not able to find a transcript for the video, sorry! (I feel the same way you do about them, but that one’s worth it)