the Stoics asserted the existence of a rational and purposeful order to the universe (a divine or eternal law), and the means by which a rational being lived in accordance with this order was the natural law, which spelled out action that accorded with virtue.
Christians believe that "rational and purposeful order to the universe" is created and controlled by God. They believe, based on the revelations of the prophets going back to Abraham, that there are clear moral precepts that are required as part of this rational order.
Vikings believed the the there was a purposeful order to the universe, controlled by a pantheon of Gods. These Gods had their moral precepts, but they were quite different from the Christian ones.
If you try to deduce laws from nature would your 'natural law' include the Judeo/Christian "thou shalt not kill" and "thou shalt not steal" or would it support the Viking 'fight and kill as many men as possible to secure your place in Asgarrd, take the spoils of those you defeat as your choose'?
If you really tried to discern laws from nature (purely) you would be a materialist. People like Hitchens and Dawkins take exactly this approach in their defense of atheism.
The "social darwinist" believes in natural law. At the height of that rejection of god-based morality and in favor of natural law someone with the pseudonym Ragnar Redbeard wrote the book "Might is Right", which posits that the only natural law is "might makes right" and the will to power, in the sense Neitzsche uses it.
The article you linked goes on to explain that "natural law" as used in the West is really "Christian Natural Law" as developed in the middle ages and codified into English law in the second millenium.
For the record, the common interpretation of this command is
“Thou shalt not Murder” or unlawful killing
killing in self defense is permitted, for example,
under the Ten Commandments
Defensive Acts of War are permitted
The Death Penalty is permitted under some interpretations as
a defensive act of society