Not a Stirling but an unconventional heat engine in which the piston, on the outward stroke and driven by the flywheels, draws a flame and hot gas into the cylinder through a valve in the cylinder head which is held open during this half-cycle.
 At the bottom of the stroke the valve is closed and the gas, now cooled by the water jacket, contracts.  The resulting drop in internal pressure allows external air pressure to drive the piston back on its inward stroke, storing energy in the flywheels.  As it approaches TDC the internal pressure rises to equal the external, but the piston continues on its stroke, now driven by the flywheels, and with any further rise in internal pressure prevented by the valve opening.
  When the piston reaches TDC the cycle is complete and begins again on the outward stroke.
  The engine produces very little useable power but does make a splendid noise due to the flame and gasses being alternately drawn into, and blown away from, the valve.