They give some information, but e.g. they do not say what the equivalent sensor area is - is it the surface area of the balls that sense the field or of the plate between the balls?
And they do not say what happens to the field as one draws power from the sensor.
From the formula they give it is clear that this E-field probe delivers current proportional to the displacement current.
If it works, it means that you can draw power from the field.
It is a dipole. A simple antena. Think of it just like a car radio antena but it is a lot smaller. It also is just a D-dot probe so the field needs to be changing to see an output.
If you are looking to transmit power, then look at Tesla's old papers and look at the new induction charging systems (like for the Wii).
According to formulas that I have seen, there is not much dependence of current received from a dipole antenna upon the diameter of the wire from which it is made.
In the case of this E-field probe the current is proportional to the area of the hemispheres. So something does not agree here.
I am looking at various ways of drawing power from the EM field, to find the best for my purpose, which I cannot disclose now.