Ah, that is true. Although he might not have had a legitimate form of justice, he is still the Justice arcana which imo he might care about his own so called "justice" in a sense of just getting back at his father and anyone who stood in his way. Light Yagami also tried to take care of anyone getting in his way if they were a burden. Which in the the end of deathnote, so called justice ended up being corrupt.
