In the video you can actually see the markings on the power supply. It states; SMSL Ultra-Low-Noise Power Supply +/- 18V 667mA. I make that out to be a maximum of 24 Watts. The specs for this amp state "6 Watts into 16 Ohm,3 Watts into 32 Ohm Headphones " so the powers supply appears to be more than capable for the intended job.
It's so easy for subjective reviewers to come up with some theory as to why a product sounds like it does to them. Here at ASR we believe in testing equipment and not spreading untested theories.
I've been here for a couple of years, and have been involved in dozens of discussions, so when you way "we" in your closing statement, that includes me. I am a person of science, but as such, the one thing I know is that "untested theories" are the absolute basis of the scientific process. If it weren't, we'd all still believe that the earth is flat.
And, my education, and decades of experience are in electronics, including circuit design and testing (what's your background?). A power supply's rated output does not tell the whole story - not even close. How well that output is regulated, its slew rate when hit with a sudden load, etc. are also important parameters.
Again, I am an avid fan of Amir, and this website, and I've made many purchases based on information from this site, but how any audio component responds to sine wave based tests does not tell the whole story, no more than how the horsepower and gas mileage ratings tells the whole story of how a car drives. I wish Amir would add more tests, such as slew rate and output damping tests. Those determine how well an amplifier responds to transients. And that's just one example.
Just as you do, I suspect there is nothing to that reviewer's theory, but I think testing it would be interesting and informative. I enjoy conversations like this, until I start getting insulted, so please don't go there.