It would make more grammatical sense, but to use 'him' in the next sentence is also acceptable because we know it is a man and the words are often used interchangeably in spoken English.

Wouldn't you prefer "them" in the next sentence too, then ?

As Mark says, it is common usage - because 'author' is ambiguous, in other words it is not clear as to whether it is male or female 'them' includes both.

:-) Of course. I upvoted. It's just strange to have "... you want to meet them—it’s only natural. To get to know him a little better."

They and them is/are used frequently instead of the singular. Also in non-binary and transgender circles, as a deliberate departure from "he/him" and "she/her".

Too fast. I thought "them" was possible because it can happen several times with different writers but when you read "him" in the next sentence, this 'them' sounds strange. Just my impression, you may disagree.