Pinker's response is shall we say interesting, first he says:

The book does not claim that the mean of the distribution of war deaths has changed; it explicitly notes that power-law distributions (such as those commonly fitted to war deaths) don’t have calculable means. Like Taleb, the book points out that empirically observed data from the tail of a power-law distribution provide unreliable evidence for its underlying parameters.

He than proceeds to demonstrate that he doesn't in fact understand the implications of these statistics by writing stuff like this:

Finally, Taleb thinks that it is damning that “You can look at the data he presents and actually see a rise in war effects, comparing pre-1914 to post 1914.” Yes, that’s exactly what I point out: great-power wars became steadily more destructive from 1500 through 1945. The turning point that marks the onset the Long Peace was in 1945, not 1914.

A power law distribution means that at any given time not during a major war it looks like war has fallen to unprecedented levels.

A hypothetical proto-Pinker writing in 1913 could similarly note that the turning point was in 1814, possibly even citing the Franco-Prussian war to show how wars between great powers are now short and limited.

Note that that looks like Steven Pinker's 2012 response to Taleb's earlier criticism of the book. I don't think it's a newly written response to Cirillo & Taleb's paper.