Stretching the book out to the Enlightenment is me, not Diamond, by the way. He only seeks to answer Yali's question, not to explain why Yali's tribe represents all of pre-enlightenment humanity. That is my own connection. The memes of the Enlightenment are just an extension of the same things that gave rise to guns, steel, and germs, a.k.a. civilization, in the first place.
I didn't watch your PBS thing yet Chanur but the gist of GGS is essentially the idea that it was geographical reasons that predominantly decided that Europe would sail around the world with GGS on board their vessels, first. It was not the color of their skin nor any particular merit of the individuals who inhabited Europe. You could have had Blacks in China, Japanese in Meso America, Russians in Carolina, Indians in Africa, and Americans in Europe, and it all would have, very broadly speaking, played out about the same. It wasn't the Europeans themselves who managed to sail across the Atlantic per-se, it waswhateverpeople would have arisen on the European continent. By virtue of the their geography, rivers, climate, size, location, native flora, native fauna, the actual physical geometry of the landmasses, and their natural resources they were the ones who had the best opportunity to flourish the widest. In essence, they found the best spot on the CivV map to plop down a city.
If you reshuffled the races back when they were first settling the globe, the European homo sapiens were always going to sail over to America with GGS, and not the American homo sapiens sailing over to Europe. No matter the particulars of their genetic varieties.