And you can build a bigger device, where the distance of the plates is 200m/200yard and the holes have 10cm/5inches and use the same wires. Or multiply the design by 100x. A much bigger device is not technologically practical, but it shows that there is a theoretical problem.
---
In their description they clearly explain that the electrons are reflected, and the protons pass though, so their design will not work. I think that if they absorb the electrons, use the protons as in a gridded ion thruster and then use the absorbed electrons to neutralize the ions, then it may work. You must use some energy to move the absorbed electrons from the front to the back of the ship because there is an electric field. This is not the device they are describing, but at least with this modification it may work.
But I suspect that that's a situation like the way in which you can compress a gas in a cylinder without raising the temperature: "all you have to do" is to move the piston only when it will not contact a gas molecule. All the molecules will bounce off the piston while it's stationary, and the temperature won't go up. However, that requires a Maxwell's Demon to supervise the motion of the piston, and it's inevitable that the temperature goes up.
Likewise, in this situation, you simply cannot avoid having ions impact the grids, and that's where power is consumed.
However, in a normal gridded ion thruster, a lot of energy goes into ionizing the reaction mass, and you have to carry the reaction mass. This merely does away with the need for that.