A: What is the Korean word for gym?

B: It is 'cheyukgwan'. (short dialogue)
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Cheyukgwan is a Korean word, so do we have to Italicize 'cheyukgwan' or put quotation marks?

It's best to italicize it -- and the word gym, too. Any word which is being used as a word, not with its ordinary meaning in a sentence, should be italicized.

http://grammar.ccc.commnet.edu/grammar/italics.htm
Scroll down and read Words as Words, as well as Foreign Words or Phrases.