It's grammatically correct and used by native speakers to emphasize an implication of moral responsibility directed to a specific person. To use the possessive facilitates the speaker assigning responsibility to "him" in your sentence example. We missed the concert because you were late. We missed the concert because of your being late. - The second sentence has a stronger note of making the person "own" responsibility for the outcome. It works even when it's reflexive. - We missed the concert because of my being late - This gives the outcome that sense of "It's me who messed up" confession.

Because here ‘coming’ is being used as a noun (gerund). The second coming of a song etc It would also be correct to say ‘him coming’ and in this sentence we’d be using coming as a verb

It is not a possessive his's. it is simply his = him coming late. "Don’t get so nervous about his coming late." "Don’t get so nervous about him coming late". Are both the same, it is not a possessive noun determiner, nor a possessive pronoun

Thank you all for the answers. It's really challenging for non-native English speakers to fully comprehend the nuances of certain grammatical structures. Now it's clear to me. Thank you all again.