The devil's in the "by extension." Trek's treatment of out near-future history has been more haphazard and inconsistent than people often realize. It's been possible to argue that there were up to three separate world-wide conflicts between the 1960s and Kirk's era.Yeah, I wasn't sure I had that quote right, but I didn't have time to check.
Regardless, my point still stands. Besides that one mention in Space Seed, and Khan mentioning 1996 in WoK, every other peice of the Trek franchise puts World War 3, and by extension, the Eugenics war, well into the 21st century.