I know I was a little confused as a kid. I didn't know why we didn't just call it the Chinese War since that was who we were fighting. I did love how the Army asked the Marines for all of the equipment that had been left behind in the Army's retreat. The Marines who had salvaged the gear and then smashed a Chinese force 8 times its size simply shrugged, "What equipment?" all while driving old jeeps with fresh emblems.
Well, the Chinese were neutral until MacArthur finally provoked them into invading. And we didn't learn jack crap about fighting against guerrillas and irregulars, since we made the same damn mistakes in Vietnam, getting more than 50,000 Americans killed in each war for no benefit other than becoming known as an international bully.
Technically, the Korean War is not over, since South Korea never signed the armistice. But apart from the battles of attrition while the diplomats were pretending to talk peace, it featured a number of wide-open sweeping campaigns that could well be dramatized in games.