Dealing with the lack of regex engine^ is such a tiny part of the monumental task of implementing C++ compiler from scratch - it's like quitting Mt. Everest summit expedition because a three-story hotel on the way there doesn't have elevator.
That's where he lost me as well, I've written a few parsers and seen a lot of compiler implementations, and almost never is a regex library a part of the equation.
Regexes aren't powerful enough for a full language, so you'll have to write your own lexer/parser anyway (or use a parser generator). And once you're going down that road, it's pretty awkward and unnecessary to try to jam in a regex library to only parse subsections.
In my admittedly limited experience, I've never seen anyone parse languages with regex for compilers. It doesn't take long to figure out that it'd be unwieldy and hard to be thorough.
LL / recursive descent seems to be the most common.
But anyway, yeah, how the heck do you sign up for such an absurdly huge task and worry that a lack of regexes is the main problem you'll be encountering?
Flex [1], too, uses regular expressions. However, the generated source that performs the actual tokenizing/lexing, does not need any library support for them as it is all implemented in the code. So even there lack of regex support in standard library would not be an issue.
^ - which he probably didn't need to begin with