Models are just serialized polygon meshes. We've been using models for demos for way longer than DX/OGL have existed. They're just another tool in the box which you can use (if you want to).
Using DirectX or OpenGL nowadays is like using the CPU: it's just part of the stack. They are probably lower level than you think: using DX/OGL isn't just doing something like drawModel(model, x, y, z), it's way lower level than that.
This demo in particular is not very different from old school demos. Back in the day we had interruptions, now we have API calls, but in the end shaders are just code. Elevated uses D3D to execute them in the GPU but that's all. And the synthesizer is apparently coded in ASM.
Even if you really miss the old school platforms there are still demos produced for them, often pushing the limits of what can be done.
Check http://www.pouet.net/ for lots of impressive demos.
Additionally, please correct me if I'm wrong, older demos didn't have nice graphics apis to call. They had to create and store what's given for free by Apis these days into their binary. I think the Amiga did have some 3d stuff?
With opengl with a handful of lines you could get a spinning cube with lighting. So much more work had to be put into older demos to get to the same point. On top of that, the demo writers really had to know the hardware well, and diving into undocumented behavior. A lot more was being calculated on the cpu back then too.
I haven't been on pouet.net in a while but I will look at newer demos.
I think farbrausch was one of the major groups who did this sort of thing https://github.com/farbrausch/fr_public