I didn't put much trust in a video showing anything useful but that guy showed it good & clear.
I see now how the circuit works and it corresponds with the little I read about the theory.
The idea seems to be to put both dc & ac at the same time through the water cell. The last coil seems to form a series resonant circuit with itself & the capacitance of the water cell, and the diode supplies the neccessary dc (& ac) pulses - from the step-up transformer.
The transformer could be used in a fly-back or a forward configuration, that is not clear, but he said it was 80 turns primary & 600 turns secondary.
It's going to take the better part of a day to wind a toroid like that..
But you don't really need all those transformers & coils to do what was done there. The oscilloscope picture showed clearly what was going into the cell, namely 30V dc & 12V ac p-p. You can achieve that with a dc-coupled amplifier & a signal generator, giving you full control of all the parameters involved without relying on some elusive resonance in coils.
After you establish what dc, ac, & frequency works best for the cell (& what efficiency it achieves) you can tailor-make a power supply to provide that.