The "over there" part comes from 저, which is often translated "that" or "that [noun] over there." 저 ("that over there") describes "that man." But in the English sentence, "Why does that man not go over there?" the words "over there" denote the destination of the verb "go" rather than describing where "that man" is. So the meaning is different.
"That man over there, why doesn't he go?"
We often hear children speaking in simple sentences like this.
Adults might say, "That man on the other side of the tennis court, why dosen't he go after/chase after the ball?" Or "That man on the other side of the street, why dosen't he go/cross while the light is still green?" Or "That man over there, at the beginning of the line, why dosen't he go away? We can see that he already purchased his ticket!"
"Not go" is probably technically correct if we don't know his destination but "leave" would be a better English alternative. "Why doesn't that man over there leave?" or "Why does that man over there not leave?" His destination doesn't matter to the speaker. They just want him to go away.