Just for clarification, is "runs after" being used in the sense of "chasing" the boy or in the sense of going after the boy in some predetermined order, like in a race?
It can be both. It can either mean ”chasing” or the literal meaning ”runs afterwards”.
What has pojken done if he runs from his dad and now his mom is running after him
efter = after, bakom = behind. Run after implies that the woman is following or chasing the boy; the boy is in movement away from the woman. But run behind does not tell what the boy is doing: The boy could be reading a book while the woman is running on a treadmill behind his chair.