The appnote you quote is in error. The output circuit waveform seen on the secondary of the transformer to the rectifiers is not a bipolar squarewave.
It is not a squarewave that is rectified to create the output voltage, it is very close to a sinewave.
A "resonant inverter", i.e. a system that converts a DC voltage into a sinusoidal voltage (more generally, into a low harmonic content ac voltage), and provides ac power to a load. To do so, a switch network typically produces a primary square-wave voltage that is applied to a transformer at a resonant frequency.
In a resonant convertor, a resonant tank tuned to the fundamental component of the square wave. In this way, the tank will respond primarily to this component and negligibly to the higher order harmonics, so that its voltage and/or current, as well as those of the load, will be essentially sinusoidal or piecewise sinusoidal.
A resonant DC-DC converter is able to provide DC power to a load by rectifying and filtering the sinusoidal ac output of a resonant
inverter.
The post-rectifier outut type of output filter components can be any combination of capacitors and inductors, but a series inductor serves a purpose which is to decouple the output so as to not detune the resonant transformer.
Resonant convertors are a good choice to achieve low EMI generation, but at the expense of efficiency
Most commonly, you see this type of convertor in laptops to provide the >1KV HV AC for CCFL displays. A simple test of your digital thermometer will reveal that the HV transformer core in normal operation quickly becomes hot to the touch, showing high magnetic core losses.