Maybe the output is not a squarewave but is a sinewave or modified sinewave that has a peak voltage 1.414 times higher than its RMS voltage. Then the transformer must be rated at (1/1.414 x 12V=) 8.5V RMS.
The transformer has a low voltage on its winding also because the entire 12V from the battery is not applied to it due to voltage losses in the transistors that power it and the output transistors might have driver transistors that also produce voltage losses.
Also maybe the transformer is cheap and produces its own voltage losses. It might have a primary that is 230V and a rated output of 12V but actually produces 14V with no load. Then turn it around and apply 12V to the "14V" winding then the 230V output is actually (12V/14V x 230V=) 197V. To get 230V out at its rated load you need a transformer low voltage winding that is 10.3V.