I think you and David have different definitions of a "startup," or at least different ideas of how fast and how big they need to grow. I think he just means something like "a small, young company with some ambitions of growth."

Your definition is certainly the usual one, especially in Silicon Valley, but I think David just wants to remind people that that isn't the only option if you have entrepreneurial ambitions, so he's using a less common but broader sense of the word. He even says as much at the end: "It’s almost like we need another word. Startup is a great one, but I feel like it’s been forever hijacked for this narrow style."