That generator is not piezoelectric. The URL the OP linked to describes how it works very well:
"The sugar cube-sized generator, a smaller version of a design already commercially available, uses cantilever-mounted magnets to induce a current in a copper coil"
Basically, magnets shake around more than the copper coils. Magnetic
flux through the coils changes, which induces a current in the coil via Faraday's law of induction.