It doesn't. This scheme uses a membrane like the electrostatic speakers, but otherwise it is quite different. In the electrostatic speakers, you load the membrane with extra electrons and then use electro-magnets to apply a varying electric field across the membrane in accordance with your sound signal. Since the membrane has much more electrons than protons, the electric field causes the membrane to move. This method requires magnets.

The system in the article does not use magnets. What they do is they make a membrane that moves when a voltage is applied between its top and bottom surfaces. Thus, the membrane can probably be referred to as being piezoelectric, although the article does not use that term. In this case you can apply the sound signal directly to the membrane and make it move, and when it moves it creates sound. Thus, this system does not require any magnets.

The lack of magnets will make it much lighter. Also, the fact that you are applying the signal directly to the thing making the sound may result in better sound quality.