It is clear that homicide rates were higher in the past than they are in modern societies. What is not clear is whether
hunter-gatherer homicide rates were higher than those of pre-modern agriculturalists. Here we are primarily comparing band-stage forager societies to other forms of social organisation/dietary lifeway (tribal gardening societies as found in much of Oceania, for example).
Of course relatedness is relative, but the argument is that encounter rates of whatever a group deemed "non-relative" were relatively low and that hostile contact was very costly/relatively unproductive. The "other" was known, cementing feelings of kinship, but distant.
The most violent societies according to your charts are post-band but pre-state with relatively high population density. That is not in contradiction with the "foragers nonviolent compared to other pre-state and comparable to earlier state societies" model.
The interesting question is whether there may have been two optima for human organisation - one at very low population density mobile foraging, the other at the point of the modern state. The modern state may be preferable to the first optimum, but the idea that it takes 10,000 of evolutionary search time to find the second hill is fascinating.