Sure you can heat water just by putting AC on it (this is actually how most cheap air humidifiers work). But the efficiency is just 100%. In this case the water is just used purely as a resistance, and the AC is responsible so that no electrolysis can take place.
But the Steam Resonator IMHO certainly didn't work on that principle, for the energy input was certainly way too small for this huge array to have any considerable heating effect with a low efficiency as 100% ;-)
IMHO, and as Stan described in the technical briefs, the pulses are always one sided, then discharged again, and then pulses are on the other side. I think, and it's also described like that in the briefs, that you could either pulse one side +, then the other side -, or one side +, then the other side +, or - -> -.
As this coil in the first pic only has 3 windings, my guess would be that he used a switch over circuit for the Steam-Resonator in the buggy.
The discharging is IMHO especially very important, when you have different polarities, for otherwise you would get electrolysis (Dr. Stiffler Circuit). If your would use the same polarity for the elctrodes and if the water is more or less isolated, the water would just one time get the charge of the corresponding polarity and couldn't discharge anymore. So also in this case a controlled discharging does make sense (which is IMHO attained with the help of the 2 NPN Transistors).
But that just my current guess. And IMHO as long as noone was able to really replicate the Steam Resonator (and with replication I mean with an OU factor) every idea is as good as the other. So I do definitely not claim that this guess is in any way correct!