anarchy is the destruction of all unjustified hierarchy, not just the government. Anarchy means no rulers, not just one less.
"What do you mean? You think the slacker owning the food that the industrious person worked hard to obtain is essentially what owning capital is in a market?"
to own capital is to control private businesses and through that control profit is extracted from the worker. The owner of capital need do nothing except own capital to survive, essentially a ruler and leech.