You can't. This is just covered by classical electrodynamics. Of course in a sense you can say anything is quantum, but then the stability of a table is quantum (which it is). If you were to have a single photon source and avalanche detector, ok now you are talking quantum.
The first 2 minutes of that video make it clear that they think it is "real" quantum effects (e.g. at 1:34 entanglement > EPR paradox > Bell's Theorem > local realism). Those are pretty quantum-y imo.
Yeah. At 9:34 they're dealing with entangled photons passing through 2 filters at different points in space, simultaneously. They affect each other, which is impossible without faster-than-light communication between them. This is absolutely quantum and cannot be explained at all by classical EM.
If you have entanglement then it is quantum. Yes. But the comment was you 'just' need polarized glasses. So if 'just' polarized glasses for a few $ means: "and of course a biphoton source for a couple of thousand $ and some coincidence counters for another couple of thousand $", then you only 'just' need polarizers.
