The paper you linked has the words "A meta-analytic review of longitudinal research." in its title so I stopped reading. If you want to summarize, I'll take your word for it.

It's controversial because it could be used to justify a number of racial or eugenic policies, and because it's sort of silly, in the melting pot of America, and with our knowledge of intelligence, to make any claims on social classes having stratified into different classes of human within the space of a few generations.

Genetic determinism isn't so clear, unfortunately. Humans having two legs is highly genetically determined, but that doesn't mean that variance in the number of legs is explained by genes; it's more likely to be environmental factors, like injuries.

Another factor is reversion to the mean. Two bright people are likely to have children dumber than them.