I think the more important split than left vs right is neuroscientist vs non-neuroscientist [0]. It's absurd to think that there would be no gender-related neurological differences, but also unlikely that there are large differences. The answer lies somewhere in between, and the more you learn about the brain, the more you realize how limited our scientific understanding of it is.
Also, seeing as how this article is pay-walled and not available on any mirror sights, I suspect that almost no one commenting here has read the article in full. Which brings us yet again to [0].
[0] https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect