This verse deals with the conflict between the powerful and the weak, in which the justice system becomes the tool of the powerful—a relevant and painful image in the Old World. The person defrauded of his property would naturally feel anger and a temptation to retaliate—almost certainly retaliation outside of the law since the law had shown itself as a tool of injustice. Jesus removes both the right of retaliation and the provocation to anger. While the coat might be taken at law, the cloak would be given freely. Giving a gift cannot be provocation for retaliation. The anger is symbolically given away with the cloak.
Because the legal situation is specific to Old World law, it is not directly relevant to the Nephites. It is not clear how they translated this instruction into their own setting.