Sorry, we'll just have to disagree about that. The Wikipedia entry for 'Magic' literally has the title 'Magic(supernatural)'. Now, in all fairness the term magic is usually linked to the
practice of magic in the form of rituals, etc. but there is no separation between what his magical and what is supernatural, magic is simply a cultural manifestation of the supernatural. Thus in metaphysical terms they are entirely cognate. When I say that magical abilities cannot be described and explained logically, and thus cannot be subject to verisimilitude, this is a principle which applies to ANY supernatural thing, not just spell casting. Supernatural fighting ability, especially when it is marked by such an illogically narrow applicability as
@Manbearcat points out, IS MAGIC. The lack of "I wave my hands to make this happen" is irrelevant.