You are talking about an unregulated market; and you also managed to contradict yourself: see "[Contradiction a]" in your quote above!
The definition doesn't have any other qualifier; it is what it is. It doesn't speak of gov:s influencing private businesses, but actually controlling/setting the price for them. I'm not talking about the end user, but about private businesses buying&selling, setting their own prices and competing; so where's the gov. regulating prices?
You are just spinning my words, yes an unregulated market is a form of free market, but a free market has to be more than that.
An unregulated market can become infested with cartels, because it's unregulated.
A free market doesn't have inteference neither from private governments (cartels) nor public governments (state).