Kids behave according to the boundaries and social structures in which they live. This includes peers and family. To the extent that they spend more time with peers, it shouldn't be surprising that a great deal of modeling comes from that source.
However, to take that and use it to assert that parents don't have important causal impact on a child's behavior is ludicrous. For one, the modeling done at an early age sets trajectories that have momentum for the rest of their lives. Second, parents hold a unique relationship of love and trust which heavily weights their input compared to time exposure as kids age. Third, the idea that parental influence drops to zero outside of "the very beginning" is simply false. My kids (8, 5) could win awards for mirroring back various parts of my and my wife's idiosyncratic behavior patterns, and that becomes more sophisticated over time. Sense of humor, problem solving approaches, how they conduct an argument, you name it. The uptake is dynamic and continuing. Tactics and methods of discipline and boundary-setting in particular are ongoing sources of input. This is blindingly obvious to anyone who has raised children of their own.
Which, importantly, Pinker has not. We should be highly skeptical of strong assertions made by someone who has no personal experience in the subject, especially on what is probably the most common human activity behind sleeping and the three F's. It's like a virgin telling me the best way to have sex after studying porn. You can't really know what it's like until you've done it.
There no doubt is a macro level where certain broad outcomes on which we have passable data are predictable by ZIP code, but those findings aren't extendable to "parents don't matter short of keeping kids alive". Humans are more complicated than that.
And how does one do that? We don't know anything about the genetics of the people in the data beyond grossly superficial aspects. And even if you had everyone's complete genome we still know almost nothing about how genetic inheritance works for complex behavior over a lifetime. Plus, you couldn't construct a controlled experiment if you wanted to. The closest we've got are the "separated twins" studies, which show large environmental drivers.
And even if this were true, it has got to be the worst possible foundational premise from which to approach parenting.