Mills is accepting the value for the intrinsic spin of an elementary particle which is a foundational assumption of quantum mechanics. Mills seems to be picking and choosing what he likes about QM and what he does not like so that the numbers that he gets works out to what he likes.
No, it's not related to QM, it's measured values the angular momentum of the electron is measured to hbar, then the precession means that what's left of the total angular momentums is hbar/2 that's happen to be the same as the intrinsic spin. So no, QM is not used, but all measured values are used.