You need an egress window in any bedroom. The purpose is to provide an alternate point of exit from inside a bedroom in the event of an emergency. Having an exterior door located nearby but still outside of the bedroom will not qualify. If the bedroom doorway is blocked, the occupant still cannot exit the room.
OK, first of all it is probably best to not get into a shouting match with the local code officials. No matter how wrong you think they are, you still need their approval. So be sure to stay civil!
Second, the question of which code version should not be up to whim. You can verify what copy of the IRC your state and local city uses by looking it up online. Many states make additional adjustments to the code, and your county or city might as well. All of this is easily verified.
Third, put down the Webster dictionary. Building codes and construction have specific meanings for many words and phrases, and a dictionary will not help you.
But to get back to your question, the answer is in the very code you cited... you just stopped reading too soon:
IRC 2009, Chapter 3
R310.1 Emergency escape and rescue required. Basements and every sleeping room shall have at least one operable emergency and rescue opening. [...] Emergency escape and rescue openings shall open directly into a public way, or to a yard or court that opens to a public way.
So it only counts as an emergency exit if it goes directly outside. It can't go up stairs and then out a door. The side door you already have counts as an emergency exit for the ground floor, but not for the basement.
Unfortunately you have learned that if you do construction in an area of the house you are generally required to bring that portion up-to-code. If you were not doing any work in the basement, it's unlikely that the building officials would care about the exit. But if you touch it, you own it.
Best Answer
As long as one of the "viable exits" meets the standards for an emergency escape and rescue opening, then you should be all set.