Wouldn't it be funny for authors to leave out one or two key points in their description? I suspect that's common.
The article suggests that a supplementary transformer can be switched so it adds to mains AC (boost, or waveforms in phase), or subtracts from mains AC (buck, or waveforms out of phase).
PWM adjusts the amplitude of voltage through the transformer.
The diagrams show an 'IGBT power stage' consisting only of transistor icons. It's not truly a working schematic. I imagine the real-life hardware is a full H-bridge. The job of reversing transformer polarity could be done by a DPDT switch, to select whether it's in phase with mains AC (adding both voltages), or in opposite phase (subtracting its voltage from mains). However today's trend is to prefer solid-state switching.