Unclear why these are called "solid state". The main innovation here seems to be bonding the piezoelectric elements to a membrane to serve as the speaker.
Piezoelectric earphones have been around for a long time; they were popular back in the old days because a crystal radio could drive them at a listenable volume without any external power source, using only the power received from the radio antenna.
How does it work? Well, instead of the coil and magnet system that's been used for over a century, MEMS drivers rely on a voltage-driven monolithic piezo drive that convert signals into sound. This design sees a silicon diaphragm used for the speaker, with the piezo layer distributed evenly under the diaphragm surface.
I'm no engineer, but that sounds different than normal speakers to me.