The paragraph is a bit muddled. I took it as pointing to American dominance at the end of the war, preventing Soviet over-reach or immediate direct confrontation with the Allies. After all, "Americas enemies" in the sense of Germany, Japan, and Italy never got The Bomb—they still don't have it, even if they could all likely get there pretty fast if they wanted to, these days—in the sense of building their own nuclear weapons, so he can hardly mean them as the enemies who got the bomb "soon after"—that's the Soviets, our wartime frenemy, and I expect nukes were a significant factor in shaping the wrap-up of that war, even if they played only a minor role in bringing the actual victory over the axis powers.

But I do think the broader point of nukes being a "you have it, or you don't and can't even really approach the capability of those who do" sort of tech is accurate.