Well, for one, KaTeX doesn't do "LaTeX" but a limited subset of the TeX equation syntax.
As such, it can't handle more complicated macros or typesetting anything apart from equations.
This is not a very good explanation, nor is it useful for anything.
A single qubit is not useful for computation and the way it is written doesn't generalize to more than a single qubit.
The code doesn't even really simulate a single qubit properly, since it doesn't use complex numbers.
What they call a "Rydberg gate" is not a gate at all.
Most of the text feels like it's written by an AI.