Since they operated directly under the wires, I think this is clearly a near field.
Generating power from far fields does not seem likely to get any meaningful yield. I remember my father showing me how to build a passive radio receiver using a strong sender nearby and it worked. No other power source involved but you could listen to the (weak) output. So in theory possible, but not really useful.
The earliest radio receivers that I built as a kid were entirely passive, eg a tuned circuit and a diode, and the captured energy was enough to drive a ('crystal') earpiece. I was many many (tens/hundreds of) miles from the transmitters.
Generating power from far fields does not seem likely to get any meaningful yield. I remember my father showing me how to build a passive radio receiver using a strong sender nearby and it worked. No other power source involved but you could listen to the (weak) output. So in theory possible, but not really useful.