Looking at the first page and not reading too much
I think it works like this: The oscillator transformer switches the pair of MOSFETs of and on in a complimentary (C)MOS fashion. On one wave of the oscillator signal say the top left MOSFET and bottom right MOSFETs are closed and the other ones are opened. As a remark I'd say that can maybe be replicated by standard CMOS.
So the small winding of the second
transformer connected to the tube get a square wave from the complimentary switching mosfets. This square wave gets rectified at the secondary leading to the tube. The resistance/transconductance of the tube determines whether current flows. More current in the tube (positive grid signal) means that an equal but transformed current flows in the smaller winding primary. This current will change direction every time though.
I'd say this might be replicated with a CMOS rectifier IC (CD4049), connecting the speaker load between the Vdd and the ground. This takes out the oscillator transformer. Two pairs get a positive square wave, two a negative (spreading the current) at say 300kHz. When nothing is connected, no current should flow to the speaker. In between them is a step-up transformer able to handle the oscillation frequency. Just simple trial and error, get something from Mouser that steps up from 9 volts to 250 volts and works at 300kHz.
I don't see right now how negative voltage swings supplied to the load work. In my head it only works with positive voltage swings. I'll think about it.
Maybe I'm overlooking something important or I oversimplify. Maybe I'm plain wrong, and PRR laughs at my explanation. It's just my 1cnt trying to understand this sucker.