That's about as precise as most dictionary definitions. It doesn't mean the actual meaning of the word is that broad, just that dictionaries don't go into excessive detail.
There seems to be varying opinions on what a startup actually is. Some definitions focus on the ability to rapidly scale, while others emphasize the fragility of startups. For instance, Eric Ries, author of The Lean Startup, defines a startup as "a human institution designed to deliver a new product or service under conditions of extreme uncertainty." This definition would tend to include almost every new business, while your definition of a startup would only include those which are structured for rapid growth. Maybe I'm being a bit too pedantic, but it seems the word "startup" is being used so inconsistently nowadays that it has lost a bit of its meaning.
The problem lies in the definition of "new" and "extreme". Both are very loose.
In the standard Techcrunch definition of "new", and "extreme", "new" is "new" and hasn't been done successfully before (or at least in the reach of the startup in question).
And "extreme uncertanty" usually means: you have a burn rate which forces you to rapidly achieve product-market fit, pivot, get more money, or give up. The above definition of "new" adds up to the "extreme uncertanty", as you are not sure what you are currently doing is something people want, and even if you pivot into something else, you will not be sure about it as well.
Therefore, a new old' fashioned bakery is a new business, but it is not doing something "new", neither has "extreme uncertainty" attached to it.
Yes, but won't that new old' fashion bakery still have "extreme uncertainty" in its successful outlook, especially in today's dire economic conditions?
The old' fashioned is not creating anything "new", by definition. If it is delivering it in some way like Zappos delivers shoes, or Uber send cabs, it is another story.
The "extreme" part usually conceives that you don't know if what you are doing is something people want. We know old fashioned bakeries is something people want. This can be seen on how much Eric Ries talk about "pivots". A bakery pivoting will not be an old' fashioned bakery.
Again, the definition is loose. Eric Ries' mentor Steven Blank has a more precise definition[1] which removes these cases:
a startup is an organization formed to search for a repeatable and scalable business model.
I don't think these definitions are made to replace one another, they are made to give different views of the same object. The same way an elephant is not a wall, snake, spear, tree, fan or rope[2].
Edit: Swombat recently argued[3] that the difference between a startup a and a lifestyle business is that a "lifestyle business" lacks vision.