The fallacy is made clear if you look at something less charged like hight. Clearly, in your town, height variance is mostly due to genetics. However, in genetically similar groups over time, heights have been gradually increasing over the generations. This increase is not because heights are being genetically selected for but because the genome codes for an organism that can grow taller or shorter in different conditions, and these places (e.g. Europe) are providing the "grow tall" conditions. Places that aren't providing these conditions are not seeing their children grow them taller.

Now, height is a lot easier to measure than intelligence, and a lot less politically weighted by the various movements to promote racial inequality. But the conceptual fallacy is the same.

Note that Gould is explicitly attacking a "races are genetically different in some substantive intelligence fashion" movement of his time, using the oddly similar movements from prior times. This eugenics thru biotech argument is not currently racially motivated, but western cultures have suffered thru a number of "eugenics by positive means -> eugenics by racism" shifts in the near past, so we are a bit twichty about it.

tldr: No studies about individual variation will tell you about between non-random subgroup variation.

Can you explain how you know this? Taller people, in general, are often considered more desirable mates. Wouldn't this lead to such people having more children which would lead to, well, average increases in height?