Point 8. Summary
1. It is forbidden for a non-Jew to kill another person. And, if he does he is sentenced to death by the court.
2. The prohibition of "Do Not Murder" (as found in the Torah) is related solely to a Jew who kills another Jew.
3. A Jew who kills a non-Jew is not sentences to death by the court (by Heaven though, this is a different matter...).
4. One can derive from the prohibition of a Jew killing a non-Jew that it is prohibited for a non-Jew to kill another non-Jew, as it says in the verse "spilling the blood of another person"; meaning that "what's prohibited to a non-Jew is never permissible to a Jew".