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.
It's a little awkward in English, unless "go" refers to a ride or an adventure.
Alice: "Hey Bob, I want to go on the DeathCoaster 3000, but I don't want to go all by myself."
Bob: "Get someone else to go with you. Why doesn't your friend over there go?"