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That's... kindof the question, isn't it?
(Disclaimer: I haven't seen the video yet. But yeah.)
That's a quantum mechanics thing. And quantum mechanics has a long history of making physicists and physics students really uncomfortable. The following two quotes illustrate just how fucked up quantum mechanics really is:
Before quantum mechanics, our Newtonian understanding of the world was really simple. We thought particles were little billiard balls floating around and bumping into each other and being attracted and repelled by electric fields and such. But nope! Turns out you can't even conceptually understand what's going on at that scale without making the observer/measurer/measurement a central feature of the literal math. But if you don't do the uncomfortable things in the math, you can't get results from the math that match what happens in the real world.
W.
T.
F.
Seriously. You're asking exactly the right question. The question that made the discoverers of quantum mechanics uncomfortable in the first place. Unfortunately, there's no one answer to it. There are a bunch.
In practice, you don't really have to have "the answer" to that question to design functioning solid-state storage devices or predict the half-life of a muon. You can just kindof throw up your hands and take it for wrote that "the spin doesn't exist until it's measured" (nor the position nor the velocity nor any of a bunch of other such properties of the particles in the system). But it's not like physicist don't still have this question in the back of their minds keeping them up at night.