What you are describing sounds to me like a pre-Proudhonian proto-anarchism; not yet fully formed to advocate for a totally horizontal non-hierarchical social structure. In modern political philosophy anarchism rejects all forms of authority, intrinsic or otherwise, and seeks to abolish all institutions that maintain authority over people such as governments and capitalism. So anarchism does absolutely mean “no government”, but this is an oversimplification and in no way a complete definition of anarchism.
no unnecessary relationships of authority
All relationships of authority are unnecessary.
The economic system with employers, employees and relationships of authority is capitalism. So would a free market system qualify as anarchism if the relationships are voluntary? No, it wouldn't. Not even if by magic employers and employees have the same market power. It would just be magical capitalism.
What you are describing sounds to me like a pre-Proudhonian proto-anarchism; not yet fully formed to advocate for a totally horizontal non-hierarchical social structure. In modern political philosophy anarchism rejects all forms of authority, intrinsic or otherwise, and seeks to abolish all institutions that maintain authority over people such as governments and capitalism. So anarchism does absolutely mean “no government”, but this is an oversimplification and in no way a complete definition of anarchism.
All relationships of authority are unnecessary.
The economic system with employers, employees and relationships of authority is capitalism. So would a free market system qualify as anarchism if the relationships are voluntary? No, it wouldn't. Not even if by magic employers and employees have the same market power. It would just be magical capitalism.