Basically, you'll need to learn to write shader code if you want to replicate this. A good place for beginners to start is The Book of Shaders[0]. It doesn't mention raymarching specifically, but it will give you the building blocks to understand it later.
Once you have a basic understanding of shaders, check out the site of Inigo Quilez[1] to learn more about raymarching and distance fields.
[0]: https://thebookofshaders.com/ [1]: https://www.iquilezles.org/www/index.htm
Today's 64k intros offload their drawing onto the GPU using shaders and a technique called raymarching which is a form of fixed-step raytracing that can be done in real time. Essentially the objects you see are painted with math: instead of thousands of vertices for a 3d fractal or a complex object, a formula is fed in to the ray marcher and it returns a shape with colors and lighting. Combining shapes using unions and intersections is then done and often the shape formula will take time as a parameter as well. To play with this concept yourself go to https://www.shadertoy.com/browse and see how shader programs are rendered into incredible scenes with astonishingly few lines of code.
For a wonderful look at the creation process, see the grandfather of raymarching Inigo Quilez create a selfie of a girl from scratch using formulas here: https://www.youtube.com/watch?v=8--5LwHRhjk
One can then generate the instructions to the 3D rendering engine and the highly custom software synthesizer in the player. This information easily fits in (less than) 64 KB. The achievement is not in the final result, but in writing the demomaker.
The German group Farbrausch (former Sanity on the Commodore Amiga) was the first to invent this procedural generation technique. Almost two decades ago, they wrote their own demomaker called .werkzeug (.tool).
Source: Wrote a tool in 1998 for our not-great-looking 64k intro "Pure" by demogroup Quad.
In "full size" demos there are often many exceptions to that: Non-procedural assets (some exported from other software) like soundtrack, models, textures, animation and so on, which really expands the possibilities, it's really just the tiny size categories that squeezes them out (maybe also that compression ends up slightly less interesting/useful than creative reconstruction?). There's also strong respects paid for achieving something that previously required a large blob of data, using a tiny amount of code, like all the cool voice synth stuff that was used to add lyrics to 64kb intros years ago (eg: Candytron by Farbrausch that was released at Breakpoint in 2003!).