Nobody suggested they originated the term. Paul Graham's definition for "startup" is exactly right for Silicon Valley, and the Merriam Webster definition is incorrect, for Silicon Valley.

It's true that lots of people use the word startup to mean fledgling business, and that's perfectly OK and cool, but if you use the term "startup", in Silicon Valley, to refer to a lifestyle business, people will view it as self-aggrandizement or delusion.

This is also true in any venture capital context anywhere in the world.