Yes the Romans adopted the myths of the Greek gods and tacked them onto their own gods, but this doesn't necessarily make them "the same". For one thing, there was not complete overlap. The Greeks had no equivalent of emperor-worship or Janus. The Roman worship system was quite different. Eventually they began to ignore their old gods, and in their place adopted Eastern sects such as Mithras, Sol Invictus, or Christianity.
Even if they had the same main gods as the Greeks (Jupiter, Pluto, Neptune), some of the subcults would be different, and the Roman CULTURE would be totally different. They would require a totally different method of gaining Favor, a different roster of troop types (no hoplites for the Romans), a different Hero system, etc.
So even if their gods had similarities to the Greek gods, the Roman civ would be quite different from the Greek ones in play. Good grief - imagine if you played a Norse civ with Egyptian gods & god powers. Think how bizarrely different that would be. The Romans would be like that, except better-balanced to work within the civ powers.