The quote is wrong. The definition of communism means that all communists are anarchist. But it does not even imply that all anarchists are communists. Anarchism is defined in such a way that it does not preclude the existence of anything but hierarchy. It can have anything that isn't a hierarchy, such as emergent relationships that are voluntary and mutually perceived of as being beneficial, such as exchange of goods and labor, and it can have money to make the establishment of such relationships easier. Furthermore, defining something out of a category doesnt define the other things In thst category out of existence, it merely shuffles them into a space where they fall under a new or existing label, and I know that once that label becomes more popular, you will try to weasel your concept back under the same roof as the one you kicked out to once again sponge off of its popularity.