Vagrancy
Game
Vagrancy is a one-against-one sword-fighting game you play in a browser. Each player drives the shoulder and elbow of a sword arm with four keys, and two more keys run the legs. Nothing is animated by hand: the arms, the sword and both bodies move under one set of physics rules. A blade that touches a fighter cuts straight across, and whatever lies beyond the cut drops off. There is a road of eight opponents, a versus mode at one keyboard, and online play between two browsers.
Everything in a fight is integer arithmetic with a single random source and no clock, so two browsers applying the same inputs stay in agreement. Online matches run with no simulation server of ours. Connection setup can still involve external infrastructure, so that is not the same as no network services.
Checked in Chromium, Firefox and WebKit.