As far as I can tell (again, in my relative ignorance), the assertion that "genetics seems to play a key role in the development of culture and social structure" is just as foolish and unsupported as the claim that you dismissed.
Would it not be completey bizarre if there were zero differences in the one most complex organ we do not understand?
Would you argue that no group of people are taller? Or could run faster? Or perhaps have varying levels of visual acuity? What would cause such differences to suddenly just completely stop because it's related to the brain?
Meanwhile, there are lots of different genetic groups making up America, even within a race - the American definition of "white" is extremely genetically diverse and contains lots of backgrounds that have formed separate identities in Europe, and you don't see a lot of cultural separation on those lines. You see cultural separation on visible lines like actual skin color, language, recency of immigration, etc. But all of that is more easily explained by humans making conscious choices to associate with certain people we think are like ourselves, not genetics.
Tendency towards aggression, as your paper shows, is an individual characteristic, and something that can be overridden in either direction by social norms. (Even within a fairly homogenous genetic group, there's a huge amount of individual variation in aggressiveness.) I'm certainly happy to concede that genetics matters a lot at the individual level, but it's a large leap to find that it matters at the cultural level. If you introduce one million people without (or with) this gene slowly into a culture of people with (or without) this gene, letting them assimilate, letting them have children and raise them within the existing culture and intermarry, would we expect a chance in cultural norms for people with this genetic background? Possibly, but I certainly wouldn't expect one.