I did not read the entire text, but I find it amusing how obsessive nitpicking leads to the idea that the Eugenics Wars and World War III are identical.
The rough picture is pretty simple IMO: Eugenics Wars happen in the 1990s, some space missions happen in the early 21th century, WWIII happens in the 2160s and after the events of FC, a bright new future begins.
There is a connection between the two wars which might lead to the confusion, Colonel Green used eugenics and killed the victims of radiation poisoning. If you add ENT's Klingon augments story and Terra Prime story plus the Khan story, you could claim that human eugenics had some pretty long-lasting effects upon Trek's fictional history.
Or you could roll it up from another perspective and claim that eugenics and xenopobia (see Terra Prime for the connection) are part of the nasty side of us which will not subside so quickly, hence the "long waves of eugenics" deep into the generally bright 23rd century.