I'm not familiar with Haskell, so to me the code looks like a mix of high-level declarative and low-level specialized constructs (e.g. skipWhile, takeWhile) interleaved with syntax noise. And it seems to be using quite a lot of external libraries. Also, correspondence of the code with the HTTP spec is completely non-obvious.
In contrast, here's an HTTP response parser I wrote in OCaml using just one library: https://github.com/alavrik/piqi/blob/master/piqi-tools/piqi_... (see lines 26 - 218).
I've just noticed that the code you are referring to is an example. Well, looking at the example, I can hardly come to a conclusion that Haskell shines for parsing.