"Capitalism necessarily creates an anti-democratic system where those with more capital will have more power than those with less capital, and can, because of this, affect others' opportunities to gain capital. It has the same result as statist capitalism. The companies in an anarcho-capitalist society would virtually become new states, as they would have the capital, and thereby the means, to oppress others. You may say that this would violate the NAP, but who's to stop them? When in positions of power our capacity to empathize with others becomes less prominent, and we are more likely to screw people over in order to gain more wealth; the same could be said about private courts and police services."
The argument misses a vital point about how companies work. You don't make money by sitting on your capital and doing nothing with it. You use it to produce goods and services that consumers want and are willing to pay for. Companies cannot make money, much less a profit, without customers or clients. Or alternately, you can increase your money by investing it, which means that it gets loaned out and used to open new businesses and expand existing businesses.
Furthermore, this concentration of power is also unlikely to happen because there's no government barriers to competition. Anyone can start a new business, even if it's on a shoestring, and build up and expand their business into different areas. So if existing companies aren't adequately serving their customers, if they aren't offering the products customers most desire, or if they try to charge too much for their products, new entrepreneurial companies can step in to take advantage the opportunity to make more money from these dissatisfied customers and steal them away from the existing companies.
Some people argue that without a government, the companies themselves would exercise their "power" to oppress people, eliminate their competition, prevent new companies from forming, keep customers from having choices, and essentially acting as a government that sold goods and services, instead of as a business.
So what would keep Wal-Mart from attacking K-Mart, stealing their goods, killing their employees, and burning down their stores? Well, for one thing, such things are an expense that take away from the bottom line, and there's no guarantee that this will encourage customers to shop at Wal-Mart instead of K-Mart, or if the customers would simply switch to shopping at Target or Sears, or Dollar General or any number of other competitors. Wal-Mart would need massive resources so they could attack many or most of their competitors, which would make the whole enterprise even riskier, especially when the other stores fought back. And if K-Mart, Target, Sears, etc teamed up against Wal-Mart, they could most likely overpower the rogue store.
So in short, using coercive power for financial advantage is costly and risky--much better to compete merely on business terms instead of engaging in war or criminal activity. There's a reason why corporations like corrupting and using government power instead of doing it themselves--it's much cheaper for the companies to have the government do the dirty work for them. Without government, the companies are much less likely to incur the costs and risks themselves.
Ultimately, what is stopping an organization from concentrating power and becoming like a government is competition and decentralization--it's simply too costly and risky for any profit-making agency to engage in. Acting like a government is contrary to the profit-making motive.