The man running over there is my brother と The man who is running over there is my brother はどちらも正しいです。文法のルールはわからないんですけど、どちらの文を言っても意味がわかります。"Who is" があってもなっかても同じ意味です。でも典型に短い文の方がいいですから、私なら "who is" の部分を言っていないかもしれません。 例えば: The child playing in the park is my son. (公園で遊んでいる子供は私の息子です。) That dog swimming in the pool is cute. (あのプールに泳いでいる犬は可愛いです)

違和感について "A man running over there... " feels appropriate only if, for instance, one was at a race where many people were running. Usually "the" is used because it is "the" specific man who is running that is being referred to. "A man" is unspecific so it only makes sense if it refers to someone out of a bunch of running people, and not specifically, i.e., the "brother" is not in sight, its more a comment about the participation of the brother in something referred to. Like "One of those men running over there is my brother". I think that's why the phrase might feel strange.

「A man running over there is my brother」は「A man who is running over there is my brother」との文意味が同じあります。省略だと言ったらいいと思います。英語はこのような例がいくつかあると思います。 例えば、 The guy standing over there is actually my friend = The guy which/that/who is standing over there is actually my friend. どれでもいいです。 which/that/whoなどの事を省略しても意味は変わりません。 参考になれば幸いです。