I must confess that when I first read the National Public Radio article (since the actual study doesn’t seem to be online), I shook my head, though “What a load of bunk” and continued to do whatever I had been doing before.
Because as a native speaker of a gendered language and accidental linguist, I know that grammatical gender does not work that way outside some very narrow exceptions. Aliette de Bodard mentions animals. I would also add the sun and the moon, who tend to be depicted as whatever their grammatical gender is. Hence, the moon is generally depicted as male and the sun as female in Germany, corresponding to their grammatical gender, while in romance languages such as French, Italian and Spanish, the sun tends to be male and the moon female. But apart from those very few exceptions, grammatical gender is just a category. No one actually thinks of a table as male or a bridge as female. The grammatical gender simply tells us which articles and pronouns to use.
Besides, there are cases where the grammatical gender of a word does not correspond to the actual gender of the object described. For example, “das Mädchen”, the German word for girl, is grammatically neutral even though it describes a person who is obviously female. “Die Prostata” (the prostate) is grammatically feminine, though obviously a part of the male body. Conversely, “der Eierstock” (the ovary) is grammatically masculine, but still a part of the female body. “Der Büstenhalter” (the bra) is masculine, though it’s almost exclusively worn by women. Meanwhile, “die Hose” (trousers, pants) is feminine, though it was the almost exclusive province of men until approximately sixty years ago. And as Keyan Bowes describes for Hindi, German also has cases where two words which are synonyms of each other have a different grammatical gender. For example, “der Kampf” und “die Schlacht” both mean “battle”, but one is masculine and the other feminine. “Murder” and “manslaughter” are both masculine in German, while “killing” and “execution” are feminine.
I don’t really know a whole lot about the study and how serious it is, though it is notable that the book in which it appears is published by Vintage, i.e. a general trade publisher, rather than by a scholarly press. But I have an acquaintance, a linguist specializing in German grammar, who would probably tear that study to bits and spend two hours explaining how the thesis is wrong, wrong and wrong again (actually, I’m almost tempted to mail him the article now).
However, I suspect that the background – as Aliette de Bodard surmises – is the odd anglophone fascination with grammatical gender coupled with the hope that there are rules regarding what word is which gender, because otherwise grammatical gender is very difficult to learn for speakers of non-gendered languages and usually requires tedious memorizing. On the other hand, I frequently have to drill it into the heads of my students that in English the pronoun “it” is used for everything that isn’t a person or an animal they know personally.