A man killed his wife and children, so he was killed in retribution for them. Why was retribution of death exacted from him?

The father is not to be killed for (killing) his child, even if it descends (further generations). This is the position of Ahmad and Al-Shafi'i, based on the saying of the Prophet, peace be upon him: "A father is not to be killed for (killing) his child." However, if a father kills his wife, retribution (qisas) is to be exacted from him if he killed her intentionally, except in the case where he found her committing adultery and killed her for that reason; scholars have differed on this specific case. The man mentioned in the question is subject to retribution by death for killing his wife.