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The article is slightly misleading, in that it suggests the mass of a particle increases as velocity increases -- the effect which you note, is small at velocities which are not an appreciable fraction of c. But the motion he is measuring is not a result of moving the capacitor.

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.

Lets say you have a centrifuge in space, consisting of a long, hollow tube with a weight, a piston in this case, free to move from one end of the tube/shaft to the other.
For 270 degrees of its' rotation you expose the piston, through the tube/shaft at its' center rotational point, to the vacuum of space.
The piston is held at or near the center point due to the vacuum, with a certain inertial mass.
For 90 degrees you close off the vacumm of space allowing the centrifugal force to move the piston outward towards the end of the tube/shaft, increasing the inertial mass of the piston.
At the end of the 90 degrees, you again expose the piston, through the tube/shaft, to the vacuum of space for 270 degrees, drawing it again towards the center of the centrifuge, reducing the piston's inertial mass.
Rotational speed kept constant during cycles.
Keep repeating the cycle.

Reactionless drive or not?