Does HAXE have a library that supports PC recording? I can only search for the support library of the mobile platform, but did not find windows
Not as far as i know.
But the great thing about haxe is… you can fix it yourself 
If your target is windows using hxcpp you can find a good screen recorder library written in c/c++ and use it directly from your Haxe application either with inline c++ or writing externs for it. Will require some c++ knowledge though.