FTA:

“It had no power pack of its own, no wires that could be discovered, no batteries to wear out...”

just to clarify the wording of your essentially correct supposition, the radio signal emanated from across the street "completely external to the device", but when this signal encountered the device, the device resonated (like an opera singer breaking a glass across a room, or even like your eardrum vibrating while listening, except EMF waves not sound) and the listeners across the street could detect the signal from this modulated resonance... so ultimately, not "completely external" to the device.

this type or degree of "vibrating resonance" is passive "signal electronics" rather than the active power electronics inside RFID, which uses a stronger signal resonance to generate power to power up an active broadcast and computing circuit.

it's not entirely unlike bouncing a laser off the outside of a window to detect the conversation inside, though that higher tech and frequencies means the system does not need to be tuned to a resonant frequency.

I think this works on the basic wave mixing principle. You mix two frequencies together and the products include the sum and the difference. My theory is this gadget was able to reflect the RF wave sent to it mixed with the sound waves from the room.