first, csgo has a rather horrible audio engine so improvements can only do so much.
second, if in general use (across all games, music, video, etc) the headphones work fine and you do not have anything like crackling, distortion, buzzing, whistling, low volume output, anemic bass (keep in mind the hd598/game one is not a bass heavy can) or similar i would say you are fine.
good onboard sound is about equal to products like the xonar dg. yes, upgrading to something like the z would result in a bit of quality increase but whether or not it is needed depends on how things are working out for you now and whether or not you can hear a quality difference depends on your ears.