쳐다보다 is a fixed, deliberate stare, stronger than plain 보다 and usually uncomfortable for whoever is on the receiving end — 나를 왜 이렇게 쳐다봐? "why are you staring at me like that?". 이렇게/그렇게 쳐다보다 fills most of these lines, because the speaker is acting the look out on camera. 신기하게 쳐다보다 is staring at someone as if they were exotic, which one line uses about people staring at foreigners. It is not a compliment.