Frankly, this looks to me like Pinker is reasoning from a provably false premise. Non-nuclear powers haven't avoided war.
The Congo War killed ~4 million people, including 300,000+ via direct killings. The Yugoslav Wars killed 100,000+. The Second Gulf War, 400,000 deaths, 100,000+ from direct killings. The Syrian Civil War is 400k and counting.
The rejoinder, I suppose, is that Canada and Spain is a first-world example and none of my are. I don't buy it. First, because the use of proxy wars is a defining feature of 20th century combat; war in Yugoslavia, Iraq, and Syria is directly linked to great-power conflict. Second, because Pinker's example is a silly one; both because war over flatfish would have been a money-loser and because Canada and Spain are NATO signatories operating under the nuclear shield of other nations. Shooting war between NATO member states is regularly described as a nightmare scenario that would escalate nuclear tensions worldwide; Pinker is naively or dishonestly equating "owning no nukes" with "lacking nuclear defense".
Pinker has been repeatedly criticized for his focus on combat deaths, and with good reason. The technological advances of war have shifted the balance of casualties from combatants to civilians, and increased the fat-tail risk of escalating conflicts. This is another iteration of the same.
As for nuclear weapons being "disproportionate to any strategic goal" and "for all practical purposes a bluff"... I hope to god he's right, but tactical nuclear weapon use is back on the table in Russia and strategists don't seem to agree with him.