Thanks, Bob. The problem with your explanation is that the inverter output is only 60 cps.
No, you have not understood Bob's explanation.
The input voltage is first stepped up to about 170V DC using a converter operating around 50~100 kHz, then the 170V DC is used to power a circuit that's effectively just a high-voltage amplifier, just like an audio amplifier, which is supplied with the 60 Hz sinewave and generates the output voltage directly without requiring any transformer operating at 50 Hz.
This solution is a lot smaller lighter than the old approach. The amplifier could be a Class D one for maximum efficiency, to reduce the heatsinking requirements as well. It could be made pretty light, quite compact and quite efficient.