The chinese political system that relied primarily on strict laws and punishments to compel people to behave is called

The answer is Legalism.

The founder of Legalism were Handfeizi and Li Si. They believed that maintaining order and control of the empire is thru powerful and efficient government. This means, rulers has to be strong, who support harsh penalties. The laws based on this idea are based on rewards and punishments.

Legalism rejects Confucianism - the idea that love and respect is the key for the society to become orderly and stable.