Your definition of capitalism is actually compatible with left-libertarianism, in the original sense of the word not Rothbard's, market socialism and other form

Your definition of capitalism is actually compatible with left-libertarianism, in the original sense of the word not Rothbard's, market socialism and other forms of left-anarchism and socialism. The only difference compared to your definition are the views on capital, which could be generalized as saying that those who mix their labor with capital should have democratic decision making with regard to that capital.