Looks deceive, those are no ordinary LEDs and that's not an ordinary switch. I have a good idea of how this was done but I may be off on the details. The switch contains a coil which is shorted using the switch itself which allows you to detect its presence or absence. That can be used to switch power to an RF oscillator which is connected to another coil, setting up a field over the green paper, relatively close to it. The LEDs contain a flip-flop + some rectification and a cap, each LED can be triggered 'on' or 'off' by completing the circuit between the legs (which otherwise function as antennae, that's why they are bent the way they are, that way they function as a dipole).

It's a really neat hack, the guy must have amazing skills if he really has that much hardware tucked away inside the guts of an LED, you'd basically have to hollow out the whole thing, then put an SMD LED at the tip of the housing and use the remainder of the space for the circuitry.

Time will tell how much of this was right if and when he reveals how this trick was done.