...by the waste heat from the shuttle return solenoid. At the beginning of the power piston downstroke, this reheated air flows into the low pressure expansion volume, helping to push the shuttle piston and power piston down past top dead center. Once the power piston passes bottom dead center, the exhaust valve opens and the expanded air is pushed out of the engine. Solenoids help pull the shuttle and power piston to their top positions to reset the cycle.
How useful an engine like this is really depends on the availability of compressed air and electricity. It would likely be a lot quieter and cleaner than an internal combustion engine, but given how affordable and efficient electric motors are, you'd need a strong case not to just use one of those.
There's no rare-earth minerals in this engine though, which is a possible selling point in extreme resource constraint scenarios.