I think that your conclusion is correct - we are the product of an evolved nature interacting with a cultural nurture. What games we play is a function of this dynamic interaction. I offer one additional thought.
If humans are genetically almost unchanged since the Paleolithic, then these genes were selected to interact with a Paleolithic environment. Our environment, our cultures, have changed greatly since the Paleolithic. One must then wonder just how well ancient genes interact with an environment for which they were not selected. Is our effort to fit a round peg into a square hole not a source of maladaptation?