Think about the word "startup." The etymology of the word means, literally, "start up [business]". A new company that has yet to prove itself is a startup. The Merriam-Webster definition is "a fledgling business enterprise."
If that's not a startup, then calling what you're referring to "startups" is very counter-intuitive.
It's as if I had referred to a recently founded car manufacturer as a "new business" and then subsequently everyone started referring to 20-year-old car manufacturers as "new businesses."