From a Chinese perspective, their initial drive down the Korean peninsula, which led to the battle in question, is seen as a general victory. Whether one enemy army corps managed to break out and escape didn't change the fact that the Chinese Army drove the UN troops well south of what is now the DMZ.

The Korean conflict as a whole was for China an intervention by an under-equipped army against a much stronger Western coalition, which they managed to fight to a stalemate.

Recommended reading: The Korean War: A History by Bruce Cumings

EDIT: Grammar stuff

I know the Marine Corps perspective but I'm curious how the Chinese view it.

Not a historian here but grew up in China, the battle of 长津湖 is well known in China. It is also one of the few Korean war histories told in school when I was young (not sure about it now)

The narrative is one of sacrifice and bravery, how the troops fought in freezing winter with summer clothing and how American firepower and logistics prevented PVA from total victory.

What is the "Marine Corps perspective"?