This study makes a causal claim (“… suggests that this association was mediated…”). The article you refer to speaks of correlation, but the last paragraph is also reading the correlation as causation.

I have a hard time thinking of how to get around all the potential confounders starting with the genetic or psychological traits of the involved women and men, that might cause both: a “traditional” stance on how housework is shared and the strength of sexual desire.

This is why I am quite skeptic that there is an interesting thing to learn here. Sadly I have not found a way to read the whole study.