Yes, that will do the job without problem. Assuming you don't want to play F.E.A.R. at 1600x1200, that shouldn't do to badly in gaming, provided you're not trying to go above 1024x768 and/or jack up the eye-candy in games.
However...
By the specs alone, yes, it's quite a bit, but with the software included, it's probably not as bad off as it might seem. Still, I would look around at other companies offerings and see what you can get for your money. I know Dell tends to run some good deals regularly, and while not everyone likes them, you might get a little more grunt for the money or pay less for something equivalet to what Sony's asking.
Hell, the
Dell XPS 600 base unit running for $1599 offers all-around better specs AND a 19" flat-panel LCD (the one to the far right) in the package. The Sony Vaio requires the monitor sold separately. If you already have a monitor, you should be able to drop the 19" from the list and save even more money.