How can a remote-controlled (wall) light switch operate without a power source?
There actually is a complete circuit; hot side of the line through the switch then through the lamp and back to the ground side of the line.

When the lamp is supposed to be "off", the electronics "steals" just enough current to power itself, but not enough to light the lamp.  When the lamp is on, again the switch steals just enough power to run itself.

This technique has been around a long time, it used to be used to provided illuminated light switches (typically using a NE-2 neon lamp), which would glow when the lamp is off. 

This only works if current can be drawn through the lamp when the lamp s off.   Obviously this works fine for conventional incandescent lamps.  I would guess it doesn't work for CFL's.  There is probably a list on the instructions.