"The authors underscore that the overarching correlation between brain volume and "braininess" was a weak one; no one should be measuring job candidates' head sizes during the hiring process, Nave jokes. Indeed, what stands out from the analysis is how little brain volume seems to explain. Factors such as parenting style, education, nutrition, stress, and others are likely major contributors that were not specifically tested in the study"

The tl;dr is their research found that 2% of cognitive differences can be attributed to brain volume, indicating intelligence is influenced primarily by other factors.

They also found that though male and female brains differed in size that didn't produce a statistically significant difference in outcomes, but the study didn't tackle this specific issue so they couldn't say much else definitive about it (the cortex construction speculation notwithstanding).

I applaud them for pre-publishing their methodology and their commitment to publish regardless of the results.