I mean this entirely respectfully, and I don't mean it as a dodge of your question, but IMO this is just too big and complicated of a topic to fully resolve in one YouTube video aimed at a popular audience, or in one Physics Stack Exchange question page. Entire books have been written on this subject. In order to fully address it, you need to spend at least a few pages just carefully defining your terms and your top-line philosophical assumptions about the basic nature of reality and of scientific theories. As rob said, being either "right" or "wrong" is too much to ask of a YouTube video on this topic. (Well, okay - it may not be possible for it to be "right" within the space of 45 minutes, but I guess it could definitely be wrong within that span of time.)

Just to illustrate the challenges: all of the quotes in your question occur between the 33- and the 40-minute mark. But then, in the last five minutes, Derek goes on to introduce an entire new conceptualization - the many-worlds interpretation - which he seems to imply is fully local. (David Deutsch, in particular, argues strongly that the MWI proves a completely local formulation of QM, albeit one that lacks counterfactual definiteness - another huge aspect of the debate that the video barely has time to touch on.)

Taken on its face, this seems to suggest that the last five minutes of the video obviate all of your quotations. But then again, Derek says "Maybe there is a way out" (right after the dramatic cymbal crash) - so it isn't entirely clear what he is trying to argue.

I think that trying to decipher this video's "true" argument is not the right way to go. It's supposed to be a fun and engaging introduction to these ideas to a lay audience, not to win over experts with an airtight rigorous argument.