There is an American law that does allow civil suits in these circumstances:

https://en.m.wikipedia.org/wiki/Torture_Victim_Protection_Act_of_1991#:~:text=L.,torture%20and%2For%20extrajudicial%20killing.

>Does the US routinely prosecute murders of green card holders when they’re abroad?

This is a civil suit, not a criminal charge, so there is no prosecution involved here.