mouse movement alone is a control input isn't it?
The NES dpad is four 'buttons' for a total of four inputs, so you could argue mouse movement is four inputs. But also there was the light gun for the NES https://en.wikipedia.org/wiki/NES_Zapper which could be used to point and 'click' any spot on the screen, so its not like using mouse input is completely crazy, just pretend its the light gun