You can see one design from the Elektroscluch . It seems to be as simple as connecting an inductor to ground and then feeding the "positive" end into an amplifier (and in your case an ADC). I don't see why you need two inductors here. This circuit uses one.
Given the sampling rate of 500kHz (if you copy the paper), you might want to put in a low pass filter around 200-250kHz anyway. On the PCB in the supersensor papre it looks like there may be an RC filter just off to the right, which maybe feeds into an op-amp buffer (unity gain amp) U8. That's a guess though, since there's no schematic.
Their conference paper does cite a couple of references that may be useful, but they seem to be more related to power line monitoring, not inductive/contactless. For example:
Both these papers show that lots of interesting emission in the low 100s of kHz which matches with the sampling rate in the paper.
Another example they cite is the Syntonistor project from CMU - that seems closer, although a lot of the conditioning circuitry here doesn't seem to be on the Synthetic sensor PCB (but who knows, we only have a photo of the top side). Also it's designed to detect 60Hz, but you could tap off the signal just after the inductor.