I'm more impressed by a brainfuck compiler written in brainfuck.
https://news.ycombinator.com/item?id=697501
https://github.com/matslina/awib
Awib is a brainfuck compiler entirely written in brainfuck.
Awib implements several optimization strategies and its compiled output outperforms that of many other brainfuck compilers
Awib is itself a 4-language polyglot and can be run/compiled as brainfuck, Tcl, C and bash
Awib has 6 separate backends and is capable of compiling brainfuck source code to Linux executables (i386) and five programming languages: C, Tcl, Go, Ruby and Java
The original was 240 bytes, and created an executable directly.
https://wiki.tcl-lang.org/page/Brainfuck
Brainfuck-to-Tcl transpiler:
Also, a parser implies having an internal, structured representation. As the C language is neither internal nor structured, I'd say the program is more likely a compiler.
It's still an impressive feat, and very informative on the assembly details - but doesn't feel as incredible as the headline makes believe as the core logic seems to be a string search-and-replace of the strings in the "reviewing brainfuck" table.
Seems to me, you could write the next brainfuck compiler in sed.