but men are the stereotypically intelligent ones

...by some stereotypes. There's also the "men are stupid" stereotype. So I'm not sure about your premises.

However, I don't think your argument is valid, either. Its structure is something like:

A: females get more words during critical period
B: females more intelligent than males
...
If A, but lots of people think !B, how could A => B be true?

Just because lots of people think that !B is the case doesn't make it the case.

And if we're talking about success in school (which the article emphasizes) then note that more women go to (and succeed at) post-secondary education than men. Fewer in STEM fields, but that appears to be largely due to stereotypes anyway, not aptitude.

I would also guess that the male-female discrepancy is much smaller than the poor-rich discrepancy.