I don't recall the carpet pattern you are looking at, but if it is a pattern that requires matching, you have to account for the overlap on the stage to line up the pattern. So, you need enough to cover the entire stage plus pattern overlap (could be anywhere from 6" to18" plus the riser height). And looks to me like there will be a pretty good amount of wastage cutting out for the steps. Remeber, you have to pay for all the carpet to do the job, not just what actually get installed. Now, if you're LUCKY, you'll find an installer that will only charge for the finished square footage...it shouldn''t matter to him if you have to buy an extra 10 yards, or whatever it ends up being.
My guess is that the guys comming up with the short sq footage are not taking everything into account and will probably then try to bump up the estimate. ANd it depndes on the pattern and wheter you can install it the long way or the acrros the room to minimize wastage. I think you'd be better ordering more rather then less and have to try to get more of the same dye lot, etc.