I think it was meant like not (A has nukes and B has nukes) rather than (not A has nukes) and (not B has nukes). Strange wording, I felt the same way too.

That's what they meant: that's what war looks like when both parties don't have nukes. It's usually the defending party which benefits from nukes the most; and both parties having nukes makes every war a very dangerous affair (if it goes unchecked, as opposed to limited like India-Pakistan).

Thats what i meant. Unles both parties have nukes, it will become a proper war where countries are destroyed

Looking at india pakistan, and ukraine russia, its clear whether you should give your nuclear arsenal up or not