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While, like you say, air supremacy does not necessarily count as victory, in conventional warfare it all but assures it. During World War Two for example the reason Hitler refused to invade Britain was because he failed to establish air supremacy. Similarly, the battle of Midway was the turning point of the Pacific theatre because the United States was able to destroy all but one of Japan's aircraft carriers. Air supremacy gives belligerents a tactical flexibility that translates to near victory. For a modern example see the No Fly Zone established over Libya.
I agree with Your_Doom. If it came down to a brawl between just RoK and KPA, the South would, if not "win," demolish the North's conventional forces.

Heart of the cards, mother***er