Native Koreans would use 저 남자는 일을 잘해요. rather than 저 남자는 잘 일해요. And, if I should translate 'that man over there' into Korean more precisely, I would use 저 너머(에 있는) 저 사람.

True that "저" implies "over there", but if "That man works well." is not accepted as a legitimate translation, that is straining too hard to teach the "over there" nuance. My guess is that if you asked 100 Koreans also fluent in English to translate the sentence, less than 10 would insert "over there." Also, the alternative word is "그" rather than "거", and the explanation DL has given for '그" is only a partial one. It is often used when the object isn't even visible, or when referring to something or someone that has already come up in the convrsation.

No 'over there' in Korean sentence. Should it read? 저 남자는 저쪽에서 잘 일해요.