In its intial release, yes, Spirited Away did show in a limited number of theaters. However, once it was nominated for the Academy award, Spirited Away showed up in regular movie theaters. Unlike Appleseed, GiTS and GiTS 2, I didn't have to drive an hour to go to NYC to see it.
Spirited Away won an Oscar for Best Animated Feature in 2003, the first Anime film to do so.