Hi Torsten,
I was approaching this with the thought: "Ian has one of these boards that works, Jonathan has the same board and it doesn't work, what could be wrong with Jonathan's assembly or parts?". I hadn't questioned the design too much since Ian told us he has one working. I agree with the points you have made but I think they would cause performance problems, not cause the circuit to refuse to run at all.
Having said that... I have seen this same circuit, including the strangely placed electrolytic cap and the PNP "gate discharge" circuit, several other places online. I have not, however, seen this in any official data sheet or app note. Now that I look at this a little closer, I think the capacitor connection to pin 7 (Ipk sense) must be an error. I didn't notice it until you pointed it out - my eyes were seeing what they expected to see, not what is actually there. It makes no sense to me to have it connected like that and I think it should be connected to pin 6 Vin instead, my thinking being that it could serve as a local reservoir of sorts (?)
As for the PNP gate discharge, I'm not sure I understand what's going on there. My impression is that when the transistor's base is pulled to ground by the 1K resistor, it would conduct until the mosfet's gate is pulled down to ~0.7 volts, at which point it would turn off. It wouldn't take Vgs all the way to 0 but it would seem to take it below the mosfet's threshold voltage. I'm not sure why the diode and transistor are even necessary, except that one online source I looked at claims it makes the mosfet turn off significantly faster than a resistor alone (cooler running?). I'd like to hear what you think about this so maybe I can learn something!
EDIT: Here is one place I have seen that boost converter circuit:
threeneurons.wordpress.com/nixie-power-supply/hv-supply-kit/