Dunking was illegal in NCAA basketball from 1967-68 season until it was reinstated in the 1976-77 season. Which means during the game in question you couldn't dunk.
At the 0:20 mark of this clip Kim runs out in transition and dunks on top of an opposing defender:
https://www.youtube.com/watch?v=Fz1FO7ImIFQ
Is that the play in question? I've never been able to reconcile it with retellings of the events because:
1. It appears the official signals and 'and one' and counts the basket.
2. It happens really early in the game, not at a pivotal moment down the stretch that changes momentum and ultimately loses the game for MU
I don't have the actual broadcast, only the coaches film of that game. So it jumps around and misses sections and has no sound. But it appears to me that has to be the instance you are referring to because how many times could the same player dunk in a game while dunking was illegal. Does that match your recollection?