But maybe reframe the cold war (korea, vietnam, contras, etc), as engagements in a long war (which harmonizes with at least some of the mentalities going on in that period). I think then the thesis of "no war" vanishes.
Like it or lump it, the logic of MAD is still inescapable. It's a real-life Catch-22 that's led to a large scale peace.
Nukes are only useful if you don't use them but project the ability to use them. As Nash equilibria go...
My worry with nukes is the black swan events. Used to be there would be a big war every few decades. Nukes put a stop to that... but what if instead of a big war every few decades, they just mean there's a really, really big war, once, after a long period of relative peace?
I excerpted the top few items that extend in whole or in part past the cutoff date of 1945 that they chose.
7,500,000 – Chinese Civil War (1927–1949)[11] 2,500,000–5,400,000 – Second Congo War/Great War of Africa (1998–2003)[17][18][19][20] 800,000–3,800,000[24] – Vietnam War/Second Indochina War (1955–1975)[25][26] 1,000,000 – Iran–Iraq War/First Persian Gulf War (1980–1988)[28] 1,000,000 Biafra War (1967-1970) 957,865–1,622,865 – Soviet war in Afghanistan (1979–1989)[30][31][32] 400,000 – Civil war in Afghanistan (1989–92), Civil war in Afghanistan (1992–96) and Civil war in Afghanistan (1996–2001) (1989–2001)[37] 350,000–1,500,000 - Algerian War of Independence (1954–1962)[38] 300,000–3,000,000[41] – Bangladesh Liberation War (1971) 300,000 – Second Burundian Civil War (1993–2005)[42] 300,000 (TFG)–500,000+ (AFP) – Somali Civil War[43][44][45] [Dates not listed, wiki article puts it in the 80s-90s] 272,000–1,260,009 – War on Terror (2001–present)[46][47][48] 202,354–282,354 – Syrian Civil War (2011–present), see Casualties of the Syrian civil war 200,000 – Colombian conflict (1964–present) (1964–present)[50] [+ many more]
I note that a lot of these were 'civil' wars. I understand the book excluding those. I am not clear on the logic behind why. I do not know of a way to define a 'major war' that is not arbitrary.
The problem isn't really the definition of "major", you can draw the line wherever you want. The problem is that you compare wars to the worst in human history and then use relativism to make other wars insignificant, thereby normalizing state violence.
If a serial killer murders 10 people it's absurd to say that is no big deal because others have killed hundreds and, moreover, he killed 20 people the year before so things are on the right track to improving.