Not using the article "the"

Its ok. The use of "the" implies an intransitive verbal phrase "TO BE".
So the sentence would actually mean
"Mr Kim was appointed TO BE THE chairman of our company

Yeah.

I think it's just a matter of context. We often speak of "the president," for example, but that it not his actual title. Obama's title is "president," not "the president." So if you were simply referring to the position, you wouldn't normally include "the."

I have no idea what Im talking about. When I was a kid in English Comp classes in Catholic Grade School, the nuns made us analyze the use of phrases and verb numbers an other stuff which I cannot recall. I remember my answers, when asked why we would use a certin sentence construction, I would say
"Cause , if we used another construction, it wouldnt sound right"

I only got away with it once or twice (NUNS COMPARED NOTES AND I WAS BUSTED BY THE 4th grade.

I was sent to Fathers Gaylan and Miczkuyn because I had Elmore LEonard Books. Father G liked Leonard's books too and ,as (boss of the Polak Jesuits, he smiled as he sentenced me to "2 weeks in the "Jug", and 2 full Novenas.

I dont recall any Jesuits being hoist for child molestation. I always wondered whether the Jesuits allowed GOOMARs

It occurred to me that it might be useful to give a couple of examples:

1. He is running for President. No "the" ("the office of" is implied)
2. He is the President. (could also leave out "the" it's optional)

If you're referring to a particular person, who happens to hold a certain office, and you want to connect him to that office, you would probably say "the ____," e.g., "He is the chairman.," but it wouldn't be required. If you're just talking about the office itself, no "the."