Except they contradict, so to me, no they don't.
That just means there is an explanation that we were not given the full details of.
I already laid out a potential explanation, that also incorporates info from SNW... the Eugenics Wars were not a single conflict. The name itself implies that. Eugenics Wars.
It just depends on some context as to how the term is used. When Spock refers to the Eugenics Wars as "the last of your so called world wars", he's speaking of the entire conflict, which culminated in WW3 and sometimes seems to just get lumped in with it. "The Eugenics Wars" could refer a series of conflicts from 1992 through the 2050's.
Except for the in the SNW timeline, where it was given a fairly definitive answer.