Since the advert clearly says "ARDUINO" and not "RC" I suspect that it just provides power to operate the relay, and responds to a logic level output from the ARDUINO rather than the coded signal from an RC RX. If it uses a PIC to convert the logic level to a relay operating value, it will probably need a differently programmed one to take the encoded signal from the RX and operate the relay.
Looking more closely at the pictures, I cant spot a PIC - 2 LEDs, 2 resistors to supply the LEDs, a diode to stop the relay back emf killing anything, a two legged device that might be a resistor giving a connection to drive a transistor, and a transistor. Not at all bad for the price and convenience, but nothing to allow it to work directly off a radio control receiver. The extra bit of circuit is what makes proper switchers cost what they do.