Actually its a case of "Read the whole article, and NOT just the headline, before leaving a comment" syndrome.
The study was presented on mice who all lived in the same laboratory in identical little cages. They were not exposed to various economic classes. We don't need to run a per-capita relational analysis on them because they were mice... living in cages. One group of mice was provided tools like an exercise wheel in their cages after they reached adulthood to provide them means of exercising, which they took advantage of. The male mice that exercised sired "smarter" offspring (details into how they make that determination are in the article) even when paired with sedentary females.
Now yes I agree with you that there is a strong relationship in humans between exercise and economic class. On average humans with higher economic status tend to be more fit. There are numerous reasons for this. However, that really doesn't have anything to do with this study. This study concluded that adult males who exercise regularly, pass positive mental traits to their offspring. You could later argue that therefore a higher percentages of kids from high economic classes will display these same desirable mental traits... which I would probably agree with, but that is an entirely different argument than what is made in this study.
So yes take the 3 minutes that it takes to read this 1,200 or so word article before leaving a comment claiming that the article is wrong.