I'm surprised Pinker failed to mentioned Christianity as a factor contributing to our modern cosmopolitan, universalist point of view. It is hard to exaggerate its role in ending slavery to take one important example.
The question is, Why did Western society become more peaceful? Maybe
the historical record supports the assertion that a certain part
of Western society (specifically, the religious part) became more peaceful, and this spread to the other parts. But, even if you can establish that this is true, it's really too proximate a cause to be a real explanation. The question then becomes, Why did that first part of Western society become more peaceful in the first place?
It's like explaining why all the dominoes in a row fell by pointing out that the first domino fell. That might be an important part of the story, but the real question is, What caused the first domino to fall?
At any rate, I don't think that the historical record supports the claim that Christianity caused the reduction in violence. The 10-fold reduction didn't happen until about 1000 years after Christianity became the dominant religion in Europe. If we want to understand what pacified Europe, we should look for causes that came into play around the time that the pacification happened. It's unsurprising that, once Europe was pacified, the dominant religion in Europe, which had presided over a thousand years of violence, started to incorporate this new ethic into its tenets.