Ah yeah, that's an issue I've been doing a lot of thinking about--- I'm finishing up a games-and-AI PhD and, gods willing, going to start soonish as a prof in a cs-and-games program. They vary a
lot from school to school, and I think we're still working out how they should be taught, and where they should go relative to other departments. Some are basically CS programs with a bit of an applied twist, some are basically media-studies programs, some are very art-heavy, some are more like a vocational degree, and many are some mixture of those.
Some of the variation is based on institutional politics, I think (probably more than it should be), but some is a fundamental disagreement over what games "really" are. The two endpoints of the spectrum of views are: 1) games are a specific type of software, like search engines or word processors or operating systems; or 2) games are a specific type of media, like films or cartoons or novels.
Mind sharing where you went? I have some first-hand knowledge of Georgia Tech's and UC Santa Cruz's programs, and am curious how others compare.