It should be changed to "the man who is coming" which doesn't sound a lot better but is 100% more natural.
The purpose of this lesson is to teach us what order the words go in. "a man who is coming" places the verb somewhere else, changing the lesson.
I disagree. The literal grammatical translation of a verb that connects the 는것 grammar is "that/who," as in 뭐 하는 사람 = the person who does something, or 되지 않은 컴퓨터 = the computer that doesn't work. It's commonly translated as -ing because in English, they're both very similar in meaning and can often be used interchangeably. However, I'm sure you'll agree that "the something doing person" and "the not working computer" feel and look unnatural to native English speakers, though they are grammatically correct with no change in meaning.
I agree with Jacob. If nothing else I think the usage and meaning is more clear when natural translations are used instead of literal ones.
Indeed! 오다 is to come, and 울다 is to cry
When you conjugate each into the "ing" or "that blah blah" form, it looks like this in each tense:
Past : 온 남자 - the man who came
Present : 오는 남자 - the man who comes/the coming man
Future : 올 남자 - the man who will come
Past : 운 남자 - the man who cried
Present : 우는 남자 - the man who cries/the crying man
Future : 울 남자 - the man who will cry