Consider a smaller company that develops a couple of established products. Or one-person consulting shops. Or contract developers, etc. In short - just add "Other" :)
I put it under non-web company, though now that you mention it, a university isn't really a "company." Seems better than "other", though, since it falls under the same general area.
But I think the distinction of relevance is web vs non-web, so what did one do at the university?
My university experience would be non-web, but I used all kinds of languages (PHP, Ruby, Python, Racket, Java, C) many of which are commonly used on the web. Plus everyone uses the web these days, so HN content is often quite interesting.
Consider a smaller company that develops a couple of established products. Or one-person consulting shops. Or contract developers, etc. In short - just add "Other" :)