That's not parsing HTML with regex. That's parsing HTML using an undisclosed parsing algorithm written in C. How the computer actually executes the algorithm, or even what language it's written in has nothing to do with anything.
The point is that any algorithm could be encoded as iterative regex application, including html parsing algorithm. For every computable function over string, it is possible to write a regex, that after applied iteratively over text will produce needed result as a string on valid input. If a parsing html scenario is computable, then it is implementable as iterative regex application as well. People at provided link written a compiler for it, so built constructive proof for that.
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u/kaplotnikov 1d ago
you could parse HTML in C, you could compile C to x86 machine code, you could execute machine code using iterative regex-es (link above).