In the push-pull transistors that drive the transformer, only one transistor conducts 12V/20A at a time. So the output power is 12V x 20A= 240W if the transistors are low on-resistance Mosfets and the transformer has no resistance. Your inverter will have a square-wave output voltage that is the proper voltage when it has no load. But its output voltage will be too low when it has a load due to the resistance of the transistors and the transformer.
Many electronic products do not work from a square-wave because they depend on the higher peak voltage of a sine-wave.