The parent post is not even the worst offender. In his (otherwise good) https://en.wikipedia.org/wiki/23_Things_They_Don%27t_Tell_Yo..., Ha-Joon Chang completely flips the meaning between free markets and capitalism.
I would say that capitalism is not only characterized by private ownership of capital, but also by free market for labor, which could be almost considered a complementary feature (other side of the same coin).
On the other hand, socialism primarily rejects free market for labour in favor of worker emancipation and participation in decision-making. So both socialism and capitalism are compatible with free markets; it's the labor market where the opinion differs.
(As a socialist, I would add, salaries cannot be treated in economics the same way as e.g. price of apples, because apple doesn't care what its price is.)
Socialism is completely incompatible with free markets. Free markets typically stop being opinionated beyond the concept of enforcing contracts/consent, i.e. people are allowed to structure their economic relationships with one another however they want, they just have to respect their agreements.
Socialism is a prescriptive ideology, it is concerned precisely with the nature of the economic relationships people make. Labor theory of value. "From each according to their abilities, to each according to their needs." Workers own the means of production. To the degree that people are able to freely structure their economic relationships with one another, then the vast majority of those relationships will look nothing like the prescriptions of socialism. To the degree that the economic relationships are made to look like the prescriptions of socialism, then the economic model would fail to be described as a free market.
This is why in a free market/"capitalist" economy, communes can exist, Mondragon can exist...because you can structure your relationships with one another however you want. It's just that most people don't like that structure. "Capitalism" itself doesn't care at all if that's the way people want to distribute equity and control of the corporation. Now, if you want to structure an arbitrary economic relationship in a socialist communist country...good luck.