See, phsycially, Subaru killed him because it was Subaru's hand through his chest (that has GOT to hurt...), but Seishioru killed himself mentally because he knew about the spell/curse and still went ahead and killed himself. Hokuto killed him spiritually because it was her curse/spell that killed him.
This brings up an interesting thought to mind...
If someone was let's say...bullying someone until the person couldn't take it anymore and conmitted suicide by...umm...hanging himself, did the rope kill him (physically it did), did he kill himself (mentally) or did the person who was bullying the person kill him (spiritually)?