The "an alarming amount of fuel goes out the tailpipe" is reminiscent of the wording associated with various fuel-saver scam gadgets. In practice, this is measured in HC emissions, which are usually in the low tens of PPM range on a properly tuned engine.
Disregarding mechanical sources, engine noise is largely caused by the high-pressure gases flowing out the exhaust with pulsations on each power stroke. The distinctive beating of a low-cylinder-count engine e.g. a motorcycle is entirely this phenomenon. To attribute the noise of a properly functioning (i.e. not backfiring) engine to "unburned fuel" is completely wrong.
The Liquid rotary fires thrice per revolution, or six times faster. The go-kart engine is designed for 10,000 RPM. That puts its fundamental frequency at a less objectionable 500 Hz.
But the go-kart video did not sound like 500 Hz -- it sounded like about 100 Hz.
As for the "alarming amount of fuel out the tailpipe" line, maybe they're comparing a two-stroke engine. I don't really know how unburned fuel affects a two-stroke's sound.