The episode gave three key specs about the old war, none of which touched upon warp drive:
1) fought with primitive atomic weapons
2) fought in primitive space vessels
3) (apparently as the result) there was no mercy given, no prisoners taken, no ship-to-ship visual communication
It's probably just as well that Enterprise went off the air. The amount of fourth season style fanwanking to make this true would have been polarizing. They would have had to create a scenario such as : "We're straining all our resources just to get something that can move in space. Throwing together ships at a slapdash pace with no time to install phasers...slapping atomic missile launchers on cargo ships and shoving them to the front.."
On the one hand it's kind of cool and on the other, great amounts of people would have bitched about the creators tying their own hands with continuity.