I believe you are referring to this:
That's a recommendation for a natural draft MASONRY chimney. Perfectly good advice for someone venting an indoor fireplace, not necessarily appropriate for someone venting an outdoor generator that technically does not require a chimney at all.
You cannot. What you need to do, is attach the stack to your structure in a way that keeps the heat of the stack from damaging the structure. Then you run a flexible exhaust from the muffler of the generator into the bottom of the stack.
Interesting. The storm before hurricane Sandy, I made something like that for my generator. I used a heavy gauge brass drain elbow to turn the exhaust from the muffler into the stack. I built the stack out of 4" galvanized vent. It is terminated on the top with a rain cap (a critical part of that kit that is missing). Mine differs from this in one big way though:
In the "Genturi", the exhaust is directed at the bottom of the stack with a gap. In mine, the smaller exhaust tube is led into the bottom of the stack, with the inner tube inserted about 16". I made three vertical cuts into the inner tube, which I bent outwards to form spacers( they look like rocket fins) that keep the tube centered. I also perforated the inner tube, starting about 4" past where it enters the stack, and then loosely filled the space between the two tubes with stainless steel pot scrubbers. This overlapping area acts like a straight-through glass-pack muffler, with the bottom of the stack still open to **** air in.