Radio transmission is quite different. It propagates as a wave of coupled electric and magnetic fields over considerable distances. What they are describing is an air-cored transformer, which uses only the magnetic induction field. One thing they are not telling you is that they are in fact also incidentally transmitting radio waves (and probably causing an illegal nuisance). They have enhanced the effect by making the secondary circuit resonate at the drive frequency. It will only work, and then inefficiently, if the distance between coils is of the same order of magnitude as their diameter, not a very practicable technology.
Now let me think, if my Bluetooth headset for my phone, with its piddly little battery and the limited energy involved is guaranteed to fry my brain cells, just what will happen if I get between the power source and my 3 bar electric fire or the electric oven?
I seem to recall some similar group of skilled grant winners claiming that we could replace domestic central heating systems with microwave generators buried in the walls or ceilings. The theory was that by tuning the microwaves to only heat the surface of the skin, it would be unnecessry to actually heat the room air or fabric since their temperature would then be irrelevant. Of course, they recognised that when you co-join "microwaves" with "Living room" most of the public would instantly conclude that they would be cooked to a turn just like the Sunday lunch.