Dragon Master is actually Japanese Dragon.
In the Chinese folklore, dragons were always depicted as benign, but capable of destructive force when provoked. This contrasts with the Dragon Master and too extent the Dragon Clan, who in the former case is tyrannical conqueror of China, and in the later was corrupted and wiped out by ambition and infighting. At first it looks like that developers wanted to portray Eastern dragons in similar light as their Western counterparts, as a fantastic equivalent to the Species Subversives trope. But in Japanese folklore, dragons are sometimes portrayed as evil, such as the infamous eight headed Orochi. So going by this, the Dragon Clan - from which Dragon Master comes from - aren't actually from China, but from Japan. The actual Chinese dragons, who had Vitriolic Best Buds relationship with Tiger Clan (as a reference to Tiger vs. Dragon trope which is literally present in the game), disappeared from the mortal plane long ago, before Dragon Clan camed to China. Not all Snake Clan members were in cahoots with Dragon Master.
There were few warriors who didn't liked that part of their clan willingly allied themselves with the Dragon Master for the sake of power. Thus they, their families and other non-warrior members of clan escaped into distant parts of China (some of them even escaped into different countries) to avoid tyrannical rule of Dragon Master. Those who didn't make it, were killed in cold blood for their "betrayal".