If you were to compare a similar map from 1970 with the current one the notion of which came first would be much more clear. Before WWII IQ was pretty evenly distributed across the regions of Germany, but during the partition the IQs of children born in East Germany fell way behind those born in West Germany. And now with reunification and economic convergence IQ scores have converged too. Genetics may play a fairly large role in explaining outcomes for individuals, but if it affects measurable differences in outcomes between large groups the effect is small enough to be drowned out by other factors.

Its a long-known, well-demonstrated effect on an individual level. A more likely causal mechanism than the kind of broad social effect in the reverse direction that you suggest is that access to quality education also affects experience with, patience with, and attitudes toward the kind of assessments used to measure IQ, thus influencing results.

(There's other wealth-related -- and, on a country-level, social-support-network related effects, too, as early childhood nutrition and other social-environment factors have an effect on IQ that, again, has been demonstrated on an individual level.)

Or fewer low IQ people. Whites and Asians in the US have a higher average IQ than the US as a whole for instance.