I am sure the square is not the bridge. The bridge is usually small serpentines that wouldn't show up well compared to the metalizations seen in your picture. The other contacts are consistent with bridge connections in these sensors. Google will give you several hits on ways they can be constructed, though I haven't seen anything specific on SMI's method. My best guess for the square is a shield, or perhaps one electrode of a capacitive sensor for the motion of the diaphram. They would then combine the results with the bridge output for better dynamic range or better accuracy or redundancy or who knows.