It's literally explained in the first line on the page, where he says he wrote it "in order to win the International Obfuscated C Code Contest (IOCCC) in 2002."

So it's not that it wouldn't work, but it obviously wouldn't have worked for that contest.

Without having looked at the code I'm guessing he used unimplemented language features in the non-obfuscated version, then re-wrote to avoid using them in the obfuscated version.

TCC, the actually useful and non-obfuscated version can compile itself of course.

https://bellard.org/tcc/

But the fact a C compiler can compile itself is not very impressive. Making it fit into 2048 bytes of obfuscated code is.