There have been many periods of Chinese history with multiple competing dynasties, including transition periods. The Later Jin, for example, who became the Qing, took three generations to defeat the Ming dynasty; and they had been around since before the Song dynasty.

THe lands and territories also wax and waned throughout the centuries. A map of the territories controlled by the Qing at its peak is vastly different than that of the Tang or that of the Han dynasty.

This is more like the game of weiqi than it is the game of chess. The endgame isn't necessarily a decisive action with a win condition, but more of an accumulation.