It might be possible, actually. A differential signal CAN be produced via a standard Arduino, though there's still the 5V logic level to be concerned about. I am guessing that his lamp was capable of a 5V-swing signal (10V, all told), but this is not a guarantee, especially if the standard does not normally support this. In that sort of case, you trust that the manufacturer made the device sufficiently hardened/overengineered so that the higher voltages do not cause damage.
From watching the linked video, the signal wires are both attached to GPIO pins of the Arduino board. If one is pulled HIGH (5v) and the other LOW (Gnd), you produce a signal. The other differential signal is provided by swapping which pins are LOW and HIGH.
EDIT: That's a Duemilanove, NOT an Uno, so the outputs might be different. (Still, one of the newer 3v3 boards would probably be safer, if you are testing this). Further, if the wires are long enough, there might even be something of a voltage drop that makes it safe(er).
The end result then uses bit-banging to emulate a transceiver using this jury-rigged differential transmitter.