Users aim at buttons they can see on the screen yet instead of air, they use a touch pad (or hover pad e.g. Leap Motion), to read the finger movements and display on the screen and press downs cause clicks. - This is similar to typing on a touch screen, only the display and touch pad are not in the same area. Since this does require a pad of some sort, you might as well put keys on it :-)
Users aim at buttons they can see but can't feel on the screen (e.g. a TV) without touching the screen and an "air keyboard" calculates the pressed buttons (based on the position of the users eyes, the fingers and the screen boundaries)? - This is similar to Logitech's Air Mouse which I own, yet do not like (it doesn't consider the screen boundaries and eye position, only position relative to non-intuitive adjustable alignment).
Users type on a non existing keyboard that they can't see of feel? - Without feedback users wouldn't know where to press.