But it doesn't mean you need to fit any of those definitions to be a Startup. Except in the mind of the author.
I run a successful little software startup that has as its first and primary goal: "Maximize Jason's vacation time". Every decision I make is made in that context. So profitability is important, as is low customer support requirements, as is technical simplicity (so I never have to cut a trip short because something breaks).
From that standpoint, articles like this that make it sound like a startup should consume your life and thoughts seem a bit silly. No it shouldn't. Not unless you want it to.
That's the cool thing about running your own business. You get to run it any way you please.