Wireless power transmission was studied in the 1970s in the context of space-based solar power.  The pitch was that the beam would have a power density somewhat less than that of sunlight, and the 1 GW receiving antenna would be like a 1 km diameter solar PV array, except that the receiver efficiency is around 90% and the microwave beam would operate day or night, with or without clouds. The idea died because of high cost of the needed space-based construction.

Now these guys are saying they can do the same thing with an antenna small enough to hang on a tower? Or a temporary mobile system?

That's not advanced technology or magic, it's smoke and mirrors.

Yes, a kW scale demo can be made to work over a short distance and this has been done.  The minimum anntena size for efficient coupling is viable, as the minum size is proportional to the distance divided by the wavelength; the space based system used a distance of 20,300 miles, so 20 miles should be no problem.  However, the beam power density is a problem for MW-scale applications; a low power-density beam requires very large antennas again (at 200W/m^2, each MW requires 5000m^2); anything brighter than a couple of suns counts as a death-ray which is a serious hazard; their proposed solution of turning-off the beam whenever a bird gets in the way sounds inadequate.  The Earth is not flat, so line-of sight does not give much range, unless the tower is very tall.  There is also a huge problem getting radio spectrum, since much of the spectrum is unusable in bad weather, and for what is left, consumers place a huge value on cellular data, video, and broadband access).