This is an odd paper. It reads like a so-so experimental game theory paper written by an anthropologist. The task was designed to produce Nash equilibria that would fit story they wanted to tell. And they as though they are surprised to see "the behavior of the two partners is only qualitatively similar to" the behavior the game was designed to elicit.

I think that the most interesting finding is buried halfway down.

"Another interesting observation is that for greater rank differences (lower k), the higher ranked individuals are prone to share an amount larger than the Nash prediction." This means that the player in the dominate position behaved more fairly then they needed to.

Given that finding I think this would be a better titile: "Hierarchy is Not as Detrimental for Human Cooperation as You Might Expect"