At the time, the best most of us got was doing FM by toggling address lines fast and sitting a radio next to the CPU cabinet (there was code to do this on the DECUS tape). -AM was out because digital devices tend to be in the constant volts place.
AFAIK the only Amiga that would have come with a DSP in a default configuration is the never released A3000+ which used an AT&T DSP3210. Prototypes of the A3000+ existed in 1991.
The major contribution of the original Atari STs to music were the built-in MIDI ports, which made it easy and simple to connect digital synthesizers, keyboards, etc. The music capabilities of a regular ST were rather constrained due to its outdated AY-3-8910/YM2149 sound chip (the SID in a C64 was more capable). Only the STE introduced PCM audio.
I guess someone more knowledgable about Amigas than me can add some facts about its sound capabilities.
[1] https://stcarchiv.de/stc1993/10/interview-atari-bob-gleadow
The Amiga, on the other hand, didn't have that (or even a synth chip), but it did have the Paula chip, which gave you the ability to play four channels of samples, which got you (generally) 8-14 bit/22 kHz output on the original machines. On that side of the fence you got a lot of trackers - four channel sequencers - to take advantage of the digital audio.
Not influencial in the way the Cube is described here, as the platforms were a class of apps was developed in, more used practical applications.
And it was used in serious modern music, as practiced in the various modern music departments on the best universities, even when they did have the big money. In Graz they had this MAX/Next setup from IRCAM and simulated opera singers, in Paris at the IRCAM which did a famous movie with it, the Neitherlands, Gent and Montreal.
They continue to work on PureData, but it began taking over the industry with Ableton then. And with all it free clones.
You're probably right that approximately noone was making rave and jungle on NeXT machines, but on the other hand it's true that approximately noone was doing academic electronic composition on Amiga or Atari, which is really the tradition that this is referring to. And these were mostly separate worlds for another decade.
Aphex Twin used Amigas, not NeXTCubes.
No love for Fairlight?
I'm not so much griping at the idea of characterizing it as a media machine, but one of the first? It's not even one of the first digital multitrack recorders.
Put their headphones on. The sound seems to come from one side. Turn your head towards it. The sound comes straight in front of you. Intuitive and neat. In all VR headsets nowadays... Very cool place.