> not sure if this is just formal language, or there is some important distinction between 注視 and 見て here.

Actually 注視 is as well the word that is used in the law that forbids people from watching the infotainment screen of a car while driving. 注視 means that you are looking at something, while exclusively concentrating your mind on this specific thing, not being aware of your surroundings.

Source:

Non-native Japanese speaker here, having lived in Japan for quite some time, and who took his driving license in Japan.

注視 definition in a Japanese dictionary: https://dictionary.goo.ne.jp/word/%E6%B3%A8%E8%A6%96/