I note that the title of this thread is “Geneivas Akum”. Akum is R”T: oved cochovim u’mazolos (an idol worshiper) who is chayev missah for transgressing on the 7 mitzvos of a Ben Noach. He or she is not “merely” stam a goy but one who ought to be put to death and one who has forfeited his or her right to exist.
That is who we are discussing!! Forget the “b’tzelem elokim” and desire to save such a person’s life by violating the shabbos!!
If Torah has no “rachmonus” on this akum’s life, where do you get the sympathy for his property?! (Other than darchei sholom and ayva – OUR benefit, rather than his).