Two questions arise immediately: Why South, and how accurate. Well, South simply was the favorite direction to Chinese culture as North is to us nowadays. Regarding accuracy we should be realistic: Without regular adjustments (astronomy was another field of Chinese excellence, and the magnetic compass was known as well) every mechanism build by hand out of wood would err sooner or later. But if drawn down winding main street on ceremonial occasions it will have served its purpose as the Emperor's miracle machine.
While the magnetic compass quickly gained world-wide use due to its practical worth (first mentioned in Europe 1188), the mechanical compass - and nothing else a south pointing chariot represents - flourished only in the chinese culture area. Whether they had any practical use at all, lies in the dark of history. But several legends tell us of travelers who found their way over long distances or through low visibility environments by means of this machines.
Nonetheless the concept of compensating deviations from a straight line of travel by complex gearing deserves our admiration.
It should be mentioned that modern navigation systems (GPS et al) use pure mechanics again to bridge the gap between to satellite sightings. The difference lies in the method used for memory: While the Chinese relied on gravity to keep direction (the pointer simply didn't (or shouldn't) move as long as no force was present), contemporary designs use high speed gyros and their inertia for storage.