"Startup" is a nebulous term with no firm definition, so these kinds of arguments are bound to happen. Some people still say Facebook is a "startup" because it has the fast-paced environment with the normal superficial cultural trappings of a tech startup (food perks, no dress code, casual interpersonal culture, etc. etc.).
Ultimately it's probably just a dumb semantic argument that's best avoided.
My simple personal guide is: when it has been around for more than 2 years, has found a viable business strategy or is certain to be around for 4 more years.
There is a discussion on this question here: https://www.quora.com/When-does-a-startup-stop-being-a-start...