No, V8's regex library is not written in C. V8 compiles its regular expressions to machine code at runtime. The availability of the compiler at runtime can be a liability for things like startup time or memory use, but can also be a key advantage in situations like regular expression parsing or packet processing.
You need a regex library to turn a regex into machine code. What the parent means is that the V8 regex library compiles them, while the one used in the C code merely interprets the regex.
(The C and C++ thing is just adding confusion here)
Regular expressions are part of the JavaScript language, so they're as much "written in JavaScript" as any other language construct.
The point is that a regular expression compiled by V8 (which is not written in JavaScript) is faster than a regular expression as compiled by some particular C compiler. Of course a C compiler could possibly be written to understand calls to a standard regexp API and compile those to binary.
