My interpretation of the data is that wealthier households weight academic success as a higher importance and as such more support is given as well as an expectation of scholastic success. I can't say I'm surprised by the results of the study. After spending so many years in school I have to remind myself that there are plenty of people smarter than me that don't have the grades to 'prove' it.
Sorry to be a downer, but I'm sure what the point of this post is. The gap between kids from high and low SES families has been exhaustively documented (try going to Google scholar and searching, for example, "income achievement").
The only interesting bit, perhaps, would have been seeing the R code which generated the figures, which the author declined to post.
Of course. Educated parents typically have educated kids. Wealth is positively correlated with education and IQ. This is a no brainer.