Anarchy only refers to an absence of government, not an absence of order. The word specifically refers to government, not order, which is why there is a different word for the absence of order, known as "disorder."
Monarchy - from "mono" and "archy" meaning "government with one ruler."
Aristocracy - meaning "government of and by aristocrats.
Democracy - meaning "government rule of the people."
Anarchy - meaning "absence of government."