I don't know if I've read the term "nonstate Capitalism", or coined it myself, but I think its a succinct way to express to normies that we are not talking about the (statist-, crony-) hyphenated "Capitalism" they experience in real life.
Can you link me to this original precise definition of Capitalism? I understood it to have been originally defined as the negation of Socialism. Which would be far from precise...