Interesting point, but I think you don't mean to say vector, but something more like 'velocity', 'momentum', or better yet, joysticks are meant to control a rate of change.
Sorry, busy today and didn't see this. Velocity is a vector, but so is position, and direction, and a whole bunch of things. Anything you can express as a fixed length, ordered, group of numbers is a vector (I guess they don't even have to be numbers). The point is that the distinguishing thing here is not the vectoral nature, but the fact that the mouse directly modifies the absolute 'direction vector' while a joystick directly modifies the rate of change of that 'direction vector'.
