I think we both have different definitions of Anarchy. To me even the word "Anarchy" is man made and describes the absence of any rule of power that is made up by man. When I say that Nature is working on Anarchy basis than I mean its working without any artificial made up law. That doesn't mean that there are no power structures in certain species like you describe bees and chimps. If one chimp is stronger than the other, than that is just a fact of physical conditions, but that is not something made up by the chimps.
When bees serve their queen, than its just the rule of their genes. But humans have an intellect and the freedom of choice and don't need to follow any made up law.