Nevertheless, the word "race" remains a useful shorthand for "populations differentiated genetically by geographic location" or what have you.

That isn't what it means. It's a useful shorthand for nothing, or at least nothing of worth. If you're referring to a particular clade, for instance, don't use the word "race" to differentiate that clade. That's just using the word wrong.

I find Flynn and Nisbett's position unconvincing. Asians are obviously different and were heavily discriminated against, yet have integrated in America regardless, and now have comparable or better outcomes. There must be a more substantial reason why Africans haven't done the same, and the most plausible reason so far for me is genetics.

Pretty much the one major argument against genetics is that people just don't want this to be the case, because it's one of the least hopeful explanations. But this is bias. Once you eliminate it, it becomes strikingly evident what the most likely explanation is.

phenotypic differences in IQ between groups are not caused by direct genetic effects on IQ ('direct' because of indirect effects like genetic effects on skin color which elicits discrimination, etc).

This in itself does not use the mal-formed concept of "race". I have no problem with assessing genetic influences on intelligence.

Famously anti-racist psychologists like James Flynn and Richard Nisbett disagree, and make claims about race and intelligence fairly frequently ... Are they misusing words?

No, they're privileging the hypothesis

I'm not aware of a simple, accessible guide to the history of science regarding race. The AAA Statement on "Race" seems to disagree with me, claiming that the concept of "race" was based on bad philosophy and political motivations instead of bad science.