ADDENDUM: admittedly my comment above is emotional. Obviously not every accident ends in the driver running over the victim several times. But from the article and from some of the comments, I got an impression that these cases are not THAT unusual, and it's not just a case of a Western newspaper publishing a sensationalist Sinophobic article.
The few cases mentioned where something happened to the driver were probably the exceptions where the victim also had money.
In the Slate Plus special feature section, the author of the article shared statistics on how frequently traffic accidents result in death in China, compared with the United States. In 2013 in the US there were 32,719 deaths, compared to over two million injuries in traffic accidents. That means that, in the United States, there are 70 injuries per every traffic death. According to China's Xinhua News Agency, the ratio of traffic injuries to deaths in China is four to one.
Secondly, think about incentives. Maybe I am hopelessly naive, but I believe that the majority of human beings have something built into them that stops them from hurting others. For the majority of humanity, you don't need laws against murder, internal morality and social pressure is sufficient. However, this is a small subset of humanity that would make RATIONAL rather than MORAL choices about murder if forced to make a choice about it. This is the reason that murder has such high penalties, for those people.
tldr; China needs to raise the expected penalty for engaging in this sort of behavior to the point that it is not rational. This isn't necessary for the great majority of Chinese (any more than it is anywhere else in the world) but it is necessary for some.