It's a bit funny to imagine him as so sophomoric that he really thought this was the optimal game-theoretic strategy, which is true only in the most simplistic scenario.
It’s well established that von Neumann wanted to kill millions of people (in the USSR), and would’ve done so had he been given the chance. That quote is not an isolated case. He was a genius with no respect for human life, he was so blindly opposed to totalitarianism of all kinds that he thought no amount of collateral damage would be too much.
By the time of him writing this, totalitarianism killed 50 million people. After he wrote this, totalitarianism killed tens of millions more. Right now totalitarianism kills hundreds of thousands and is very likely on path to kill millions. So looks like he was on point with his math, again.
I don't know when von Neumann gave this advice (he died in 1957), but estimates of the death toll from a nuclear war in the late 1950s ranged into the hundreds of millions, and that's only from the war itself and not the lives (and opportunities) lost in the aftermath. https://thebulletin.org/2023/01/cold-war-estimates-of-deaths...