There are chips that allow you to gather and store miniscule amounts of electricity from surrounding RF radiation. Bluetooth LE is also designed to be a very low-power devices, so it is within the realm of possibility for this particular project.
So the LTC3105 [1] looks to be able to supply 0.060 amps at 4 volts. Bluetooth LE [2] seems to use about 0.015 amps at peak (voltage not listed). If I am reading this correctly, it is possible. The question is: what actually runs the circuit connected to the Bluetooth transceiver?
Yeah BLE uses about 12 mA while transmitting or receiving. But it does not do that continuously. Its average power consumption can be under 100 uA very easily.
However, there's no way you'd get even 100 uA by harvesting RF energy in a package that small.
I think the product is very much possible with current tech. I can't tell if the creators know how to do it and just used less technical language or if they have no idea what they're doing. At any rate, there have been way crazier scams on Kickstarter (raman spectroscopy tells me nutrition info etc).
Didn't Kickstarter ban showing mock up or rendered hardware as substitution for the real thing? Maybe that's all this is?
Your first cite link is wrong. Despite that, looking up the LTC3105, it is a maximum power point tracker, meaning that it is for DC power sources, not AC ones like RF. It also requires a minimum working voltage of 225mV, which is much higher than that generated by RF, especially with such a tiny antenna.
There are chips that allow you to gather and store miniscule amounts of electricity from surrounding RF radiation. Bluetooth LE is also designed to be a very low-power devices, so it is within the realm of possibility for this particular project.