That's a market economy, which may or may not be capitalist. Markets have existed for thousands of years under various economic systems.
Agree on your other points though, 'capitalism' was coined to just describe and criticize the system they saw emerging, one of private ownership of the means of production, combined with wage workers who do not own their tools or the product of their labor, but instead sell their time.
But its hard to have discussions around because too many people conflate "market economy" == "capitalism" but you can have markets in a feudalist, socialist, communist, any other society, that doesn't inherently make them capitalist. But I still think its useful as a term, but only to specifically describe who owns the capital.
The major issue is the "private ownership of the means of production". While some argue it's a recent development, others (like me) argue it has been present since the dawn of civilization and, ignoring the "free market" and "voluntary transactions" part, one could argue both feudalism and socialism are capitalistic systems, with the latter often receiving the term "state capitalism", instead.
And then there's the issue of "wage workers". Workers who own their means of production (i.e. freelancers) are still often considered "capitalists" themselves, as under the umbrella of "small capitalists", even if they rely more on their labor than their ownership.