EDIT: There is also one huge gaping hole in my system. What does magic do!?
Like your other attributes, magic could determine how the character reacts to in-game tests. If Strength is the character's method of testing against moving a large, heavy object, then Magic could be used to test how effectively the character resists or defends against magical effects, the power level of their own magic workings, or even something as odd as a form of "luck" or something. Make it MAGICAL!
But if you find that the Magic attribute has no in-game effect that supports your concept and design, cut it with extreme prejudice!