What is the cause of turbojets'/gas turbines' high power to weight ratio compared to piston engines? They certainly use a generally less efficient thermodynamic cycle.
Turbojets and turbofans support extremely large mass flow rates of air & fuel through them, relative to their weight. (The majority of the work performed by burning that fuel is taken up by running the compressor stage of the engine and what's left over generates thrust.) In comparison, piston engines cannot support similar fuel burn rates relative to their weight.