[Sniffnoy]

You're reasoning based on a name. Names are not necessarily accurate descriptions. From what I've read of theirs, it doesn't seem that anarcho-capitalism would support capitalism in the sense you describe.

Remember, "capitalism" is an overloaded term. Sometimes it means what you describe, and sometimes it means the free market. Make sure you know what sense it's being used in in a given context, or you can't have a meaningful discussion! In the case of anarcho-capitalism, it refers to the free market. (But even though that works out in this case, you really should be wary of reasoning based on names.)