Lower IQ correlates with lower height regardless of fucking relatives.
So culture plays no roles here, it's genetic.
Huh???? Sorry but that is completely invalid reasoning. First, they don't even show in their study that offspring of incest that were shorter were the same that had lower IQ.
It is fully possible that some of these people were shorter and some had lower IQ, but not both. Regardless, as is true for most correlations, IQ and height are correlated for a number of different reasons. The fact that they covary independent of cousin fucking does not in any way limit the various causal pathways that could connect them both to cousin fucking. For example, having a low IQ could cause cousin fucking and low SES, which in turn causes poor nutrition and thus low height and IQ of offspring.
Nothing in the study or in the general height-IQ relation outside this study rules out this or many other alternative causal explanations for why height and IQ are each correlated with cousin fucking.
A good start would be first to partial out the variance in height, and see if this eliminates the correlation between cousin fucking and IQ. That would at least tell us that the all 3 variables covary together, and at least begin to limit the now countless plausible explanations and possible causal models consistent with the data.