There are two main problems with Pinker's thesis.
First, he claims to show a tendential decline in war. But most casualties of war are the result of a small handful of apocalyptic wars: the sixty years wars, the Napoleonic wars, and the world wars. Each of these events has been bigger than the last. The consistent pattern is for there to be fewer wars over time, but for these apocalyptic wars to become more destructive. Clearly, that's the result of technological progress. If we extrapolate this trend forward, it would suggest that there will be an apocalyptic war in the next century that will destroy most of the world. Pinker acknowledges these long-tail events, but minimises or ignores their significance.
Second, his case is built on the back of a few remarkable trendlines: fewer wars, declining violence, better governance. Pinker does this very well. It's convincing and insightful. But these are data without context. Pinker's argument has no historical or sociological depth. If you want to understand what's taking place in the world, you have to recognise how the forces of modernity - capitalism, nation-states, techno-science, individualism - have led to both everything Pinker celebrates (pacified populations pursuing commercial gain in well governed centralised states in a globalised world) and a whole host of dangers (increasingly destructive technology, competition between nation-states, inequality and Darwinian economic competition, decentralised capitalism, climate change, and the destruction of nature, etc.).