It's an awfully broad period of time, though. WWI and WWII seem to be associated with their "traditional" duration, the one coinciding with the geographically narrowest interpretation. WWII is discussed in terms of 1941-1945 on several occasions, rather than in terms of 1931-56 or whatever. And there's never any attempt at blending WWI and WWII together after the fact. The most "violence" being done to the definitions is that the Great War gets its name retroactively changed to WWI, which is quite a bit different from taking a dozen small or medium wars and combining them into WWIII decades after the first ones are over.
A "general era" that spans 1993 through 2053 at the very least is very general indeed!
Curiously, one would think that "Eugenics Wars" would be the alien name for the nationalist-racist conflict we call WWII, but it's Spock who speaks of World Wars and McCoy who brings up the other name. Although perhaps both sides are ridiculing the silly terminology of the other here?