The net force is always going to be quite tiny. Objects don’t significantly change mass until they are near light speed. Even then I suspect the change in momentum due to the effect is balanced out is some way I have not thought of yet.
The effect he is using in his capacitor is the mass-energy equivalence, which comes from the same relativistic derivation, for which E = mc2.
By increasing the charge on the capacitor plates, he is increasing the electric field between them, thus the stored energy in the capacitor (CV2/2, C: capacitance, V: voltage) which amounts to an increase in the "mass" stored in the electric field. By moving the capacitor within the torsion balance, the plates move by differential amounts -- according to his theory -- as the electric field reverses.
It's still a small effect, but it doesn't depend on increasing the mass by actually moving the capacitor. The motion of the capacitor is only used to produce torsional changes to show that a differential force is being produced -- thus an acceleration without reactive mass.
I'm skeptical of the explanation given here. Popular science articles are usually barely worth reading, but I'm distrustful of any article that talks about "increasing the mass" of an object relativistically. Physicists simply do not think in those terms with respect to relativistic effects anymore, and haven't for a very long time. I haven't been a working physicist for thirty years, and it was already out of fashion for at least twenty years when I was still plying the trade.