I think that map simplifies things too much:
1. Not all water is the same. China has some of the most polluted water in the world
2. Distribution of water. Much of northern China has per capita water volume is well below the acute water stress level of 500 cubic meters per capita and requires expensive water diversion projects to keep them running. While they are indeed not as blessed with water as southern China, much of the water stress is of their own making:
Chinese agriculturalists are incredibly wasteful with water. China's water productivity is over 7x less than high income countries and below even the majority of middle income countries (I think rice crops bring the value down because of their immense water usage). Coal for power generation, which predominates in the north, and in China as a whole, is a large generator of water stress. Just addressing these two points would bring about far more improvement than all the water diversion projects combined.
This video explains it quite well I think: