為什麼 "such as being late for class" 的be要用動名詞？這基於什麼文法規則？

Such poets as Milton are rare. = Poets such as Milton are rare.（名詞Milton)
No machine can work without a fuel such as coal or oil. (名詞coal/oil)
such (...) as = 像...這樣的東西

as是介系詞，後面的字是其「受詞」，只能用「名詞」性質的字。

所以你的例句裡的「動名詞」都是動詞所衍生的，有名詞性質，才當介系詞as的受詞（動詞是不能當受詞用的）：
being late for class 是一個狀態
going to class unprepared是一個行為

正如你自己理解這些例出的是"事項"(名詞)，但是它們並不是"物件"而是人的行為或事態(acts)，所以把行為寫成"名詞"(一件事)時，便用"動名詞"(Ving)[Gerund]

補充：e.g. Certain acts on the teacher's part are also considered as in-disciplined, such as being late for class, going to class unprepared, being inconsistent, threatening ...
例句裡的舉例事項都用Ving的形式，為什麼呢？