They're highly non-linear wrt amplitude and frequency, in a pleasing way.

This makes them almost instruments in their own right. When playing a guitar through heavy tube distortion, the tubes react to your playing very sensitively, just like the guitar itself does.

When people describe random pieces of electronic equipment as "musical" this is usually what they mean.

This applies to IC amps as well, but not to the same extent. The recent history of music tech is a story of working hard with esoteric techniques to produce amazing music from primitive gear in the 60s and 70s, then inventing more reliable and repeatable techniques using digital technology in the 80s and 90s.

In recent years, people are realising that the man-vs-machine-vs-physics attrition of the mid to late 20th century actually led to a certain sonic complexity that has been missing in recent years. So now we see these hybrid products which merge old and new technology to get a deep sound while retaining reliability and a good workflow.

See also: analog voltage controlled oscillators which automatically tune themselves using digital clocks, and compensate for temerature changes.

(Incidentally, a lot of audiophile nonsense stems from them making category errors between their puported search for crystal clear reproduction, and studio engineers' quest for signal distortion with emotional quality. This is similar to how MBA types cargo cult programming terminology.)

I will expand on a comment below. Tubes usually distort with even order harmonics which means the distortion is usually in key with the note and our brains find this distortion pleasing. Transistors distort with odd order harmonics which sounds more dissonant and harsh to the ears. Transistors also tend to be clean or clip, there is little to no build up. Tubes saturate gradually and can make things sound "warmer, fuller and generally awesome". Not all tubes are great though and it doesn't look like these are power tubes so it would be for preamp/line level gear only. Either way I'm really excited to see this.

I don't see where the article says that they are. It says that the tubes are designed for musical instrument applications to generate rich harmonics. Essentially, the distortion characteristics of a tube amplifier are different from those of modern designs, and these characteristics are sometimes desired in for example guitar distortion pedals.

Korg has previously released synthesizers and a sampler using vacuum tubes for effect rather than to make them "better" in any objective sense.

it plays into that old joke about audiophiles listening to hardware. Perhaps the distortion has properties that ICs fail to emulate, or likely put three of these guys in a room and a blind listening test will have four results.

They're even-order, mostly 2nd harmonic.