The story
From anarchy (“a state of lawlessness”) + server. Unrelated to the political philosophy of anarchism.
Etymology from Wiktionary, CC BY-SA 4.0.
anarchy server
Today it means: A player-run server or world with virtually no rules, allowing total freedom for actions like hacking, griefing, PvP, stealing, and exploiting, creating a chaotic, Wild West environment where survival is difficult and the goal is often to endure or exploit the lawlessness for personal gain. Full definition →