I think there’s a distinction to be made between “deterministic” as meaning “able to be predicted in practice (or even in theory)” and “deterministic” as meaning following deterministic laws. The universe is clearly non-deterministic by the former meaning, but deterministic by the latter. The latter implies only that, to the extent that we know a system’s initial state, we can predict its later states. It doesn’t mean that we can predict the state of the whole shebang, or practically speaking even any macroscopic subsystem.
The video says “measurements” are non-deterministic but that’s misleading. Measurement would have to include every interaction between different systems. This is a whole other box of cats, and it’s very glib to gloss over this whole “measurement problem”.
But would you not at least agree that the wave function evolves deterministically? Because this is I think the “weak” interpretation of what the video is claiming. On this reading it’s just saying that quantum states evolve deterministically - a true statement that many people with superficial knowledge of QM do not understand.