Yea generative music is totally a thing. One of my favourite examples is disasterpeace.com/blog/january
You can create audio on the web using the Web Audio API. However, there are more specialized tools for this. For example, Ableton, nodalmusic.com/ or supercollider.github.io/
That said, I don't have much experience with this. There is a getting started tutorial on Coding Train: youtube.com/watch?v=Bk8rLzzSink
I did a write up on Sonic Pi for writing music with code. And it can be used for live performances with a file on a loop that is changed in real time.
Very cool, I love the example you shared.
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