This would work on a locked-down corporate PC where one couldn't install random applications.
Exactly; it just emulates an USB keyboard and sends keypresses.
Maybe because something needs to be at each end, to shine a laser at one end and to detect it at the other. Or you could use a reflector, but that's still two objects.
You don't need a reflector in the majority of cases, shining an IR laser onto a wall/door frame a couple of meters away is usually a big enough bright spot to drive a phototransistor pointing at (nearly) the same spot.
It's not using the TX and RX sides to form a beam, it's using a ToF distance sensor.
Usb dongle as keyboard send keys and I think he's using a nrf24l01+ for wireless comms