It implies that the Eugenics Wars came much later than "Space Seed" indicated.
There would seem to have been more than a single "Eugenics War" in the Star Trek universe. In the Enterprise episode Hatchery
, Jonathon Archer mention that his great-grandfather fought in the Eugenics War in Africa.
The episode was set in the year 2154, and Archer would have been about forty years old.
So a second Eugenics War around the 2080's sometime? Thirty years following the third world war.