The title (above) is a bit of article-hyping clickbait. The article is based on the book The Gendered Brain by Gina Rippon.
My reading of this article (I haven’t read the book) is that it’s not saying that there are no in gender-based differences between human brains but that the differences ascribed to sex and gender haven’t been adequately separated from the developmental influences of our strongly gendered society on our highly plastic brains. Our brains develop and change throughout our lives and many changes are driven by our experiences – what we consume, observe, practice, think, etc. If a set of people of the same sex or gender share some particular brain structure it may be that the structure develops in response to the set of common experiences as people of that gender and not because the brain structure dictated the gender of that set of people.
This article is worth reading.
Update – Here is a more in-depth review of this book.