A startup exists to make extraordinary profits by arbitraging a temporary economic disequilibrium by doing more than anyone thought possible with less than anyone thought possible; the industry is irrelevant.
I was just trying to provide a heuristic to answer your question. I don't think it's black and white though. As for Threadless, I do think it's a startup because they invented a new process to fill a temporary market disequilibrium. But if another company came along and did the same thing then I'm not so sure.