As I understand it, the rubber being is forced into the shape of a dome via air pressure, which makes one side a bit bigger than the other. The electrostatic charge on the opposing faces when one is bigger than the other would cause it to flex - acting as a speaker diaphragm.

It's a bit of a guess though; its definitely outside my wheelhouse.

Like an electrostatic speaker the opposite charges' attraction generate movement. The difference is in an ESL one of the charges are stationary. In this new scheme, both charges are on the membrane but on opposite sides where attraction compresses/thins the rubber causing it to expand along its planar directions causing the dome to get larger. The inner air pressure is to assist the expansion movement.

Don't confuse magneplanar speakers with electrostatic speakers. Other than them both being flat they are quite different beasts.