If you are born in China to Chinese parents, China considers you under it's jurisdiction for life. You can't travel to another country and start working against Chinese interests without consequences.

That's not true. You can renounce your Chinese citizenship and it's actually required if you acquire another citizenship.

This is sort of true. China can forcibly reinstate Chinese citizenship at their own discretion.

I guess in the same sense that the U.S. considers they have jurisdiction globally. Not de jure, but a de facto reality.