Yes, the links between parent IQ and child IQ are well established. Charles Murray is attempting to link IQ to financial outcomes. Those are not the same things
The article in the OP had nothing to do with this idea. It was about parental IQ, income, and SAT scores.
Murray was summarizing a study that found that parental IQ is a better predictor of Little Johnny's SAT score than parental income.It does, indirectly. If the regression
child_IQ = a + b*parent_income + error
has a positive and significant "b" coefficient, but the "b" coefficient in
child_IQ = a + b*parent_income + c*parent_IQ + error
is much smaller, it's because the parent_income and parent_IQ variables are positively correlated. This idea upsets many people.
