I buy the 'grow rapidly' part - but what does venture funding and hiring part have to do with it? Take 37Signals (your own example) as an obvious counter example.

I'd argue that 'scalability' is an important component of a startup though. I don't think anyone would consider a consultancy to be a startup - although many do meet your three criteria. They don't scale since there is an upper bound to revenue per employee (while a software product/website has no such bound).