The article claims to explain this without reference to the "spookyness" of QM, but in fact it uses an analogous projection postulate as the QM version. After t

The article claims to explain this without reference to the "spookyness" of QM, but in fact it uses an analogous projection postulate as the QM version. After the polarizer, the photon state is projected onto the "measurement" of the polarizer, and in the article's figures the author does the same which leads to the same conclusion (kind of obviously). What QM brings to the table is the explanation for what happens particle-by-particle.