I was talking with someone about this just today! Basically, if you play on the Alpa/Beta Map there is no Dominion War because its not possible to make contact with the Dominion. The only time the Dominion comes into play is if you play on the entire galaxy map and meet them either through the wormhole or through natural exploration.

Personally, I really don't like the galaxy map because in the 2260s its possible that the Federation has already explored parts of the Delta and Gamma quadrant and very common for Federation territory to reach the center of the galaxy. That just is too uncanon for my taste so I typically sticks with the Alpha/Beta map and just imagine I am fighting the Dominion if there is a war with the Cardassians in the 2370s.

UPDATE EDIT

I hadn't played the game in almost a year and saw just now there is a new "Dominion War" story arch. Does thjs activate on the Alpha/Beta map? If so, that's awesome.