It totally depends on the experience-level of the person building it, and
whether that person has the appropriate environment, tools, and test-equipment,
for building such a sophisticated device.
You won't save any Money building one yourself, but
it could be a valuable and entertaining experience.
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The circuit might be OK, although I did not analyze it in detail.
The bad news is that NOT ONLY is LQC totally correct in post #2, it is not likely to function correctly even if you do assemble it without any errors.
Consider that there does not appear to be an explanation as to how it works, which is vital for finding problems. While there are descriptions, the details are not adequate.
On top of all that, consider that what you get mostly is construction instructions.
I would totally avoid not only this project, but the entire venue.
If you want to study the circuit that is one thing. But to actually produce a useful inverter is a totally different thing.
Separately, it is possible to assemble a resonant filter to provide a reasonable sine wave, and drive it with a cheap inverter. That is an approach that does not get much attention. And to provide a less than perfect sine wave is even simpler.
A lot depends on the transformer. The leakage inductance and the output capacitor form a 2nd order low-pass filter to remove the carrier frequency from the output. The transformer must be designed to provide the correct amount of leakage inductance.
Regarding that transformer: It did not really say much about it in the cartoon show, did it??
Ian0 is totally correct about the transformer being quite important. Funny how they missed that detail.