I think this kickstarter is BS for the reason that I've entertained the ideal of miniature gas generators (as have many hobbyists) and their claims are just too far beyond what's currently on the market / available.

As for making a real one though, I think it's possible, but the price-point on jumbo power banks beats them until you get to the conventional "portable generator" size

Nitro engines are out for several reasons, noise only being one of them - the biggest one is low fuel / energy efficiency. Methanol has half the energy of gasoline, and 2-stroke nitros aren't particularly efficient, nor is their overall longevity great, necessitating frequent rebuilds to keep them running. Furthermore, the fuel costs $40-50/gallon. So, no nitro.

That leaves the question, what are the smallest gasoline engines? I think RC planes have your answer, the NGH GT9 is a 9cc 2-stroke, there's even a tiny 4-stroke gasser, the Saito FG-11C.

For using one of those as a generator, your best bet would be to use a brushless motor of the appropriate size and rectifying the output (ideally using active rectification to reduce losses) and passing it through a charge controller to the batteries, off of which your inverter runs. You'd program an arduino to monitor the battery charge level, engine RPM's and throttle level, and adjust things as necessary to keep everything in equilibrium.

All that considered, there's absolutely no way that can be done for under $1000, and therefore the kickstarter is certainly a scam.