/diy/ - Do It Yourself

So there exists this thing: https://pavlok.com/

I know it's retarded, but the idea is interesting to me. Thing is I'm not going to pay 150-200$ for what can be archieved with a rubber band on your wrist, so I want to build a similar circuit. Online there seems to be pic related as a suggestion. Thing is would this even work with DC?
Is the "pulse" from the pushbutton enough that the transformer works?

Why did they connect the transformer sides with each other?

And is there any way to get a transformer like that that's really small? Best guess I have is a audio transformer, but even those are somewhat thick.

Or is there a better way to build a small shock circuit that doesn't kill me AND doesn't cost 200$