It's possible that the writers conflated the Eugenics Wars and WWIII.
So did the writers of Space Seed.
Honestly I'm not too bent out of shape if they ignore the other shows and movies I really only care about consistency towards Star Trek (2009) and Star Trek Into Darkness and a lesser extent with Star Trek the game if it comes up and even at that only in so far with how consistent any Star Trek production is with another Star Trek production.
I'm not too worried either. Treating the Nu-Universe as its own isolated universe is the only way I can stay as sane as I was before the reboot, which isn't saying much.
Then my Youtube Star Trek comic includes B5, Alien, and Alien Nation. I'm going to see if I can work in Farscape and Twiki from Buck Rogers. I'm clearly in no position to throw stones