The word 라인 is definitely not a newly coined word. It's been used to indicate a faction or a close relationship in the past. For example, there are mainly two types of officers in the Korean army. One is from 육군사관학교 (Korea Military Academy, equivalent of West Point), the other is from ROTC. When you say,
그는 육사(short for 육군사관학교)라인이야. He is a 육사 line.
It means he is powerful and well-connected with those senior officers who graduated from 육군사관학교 in the army.
그는 김장군 라인이야. He is a General Kim's line.
It means he has good relationship with General Kim's followers and junior officers and he is powerful.
Since a decade or so ago, the word 라인 has been used to mean "a group of followers" among comedians and MCs. For example, if comedian A is 경규라인, he is a close friend, 후배 (junior) or followers who want to appear as a co-host or regular guest on his show.
The 라인 in 93라인 or 94라인 basically means the same thing. If you are a 93라인, you belong to the same group of entertainers (idols, comedians, etc.) who were born in 1993. 93년생 was used before 93라인 became popular and I think 93라인 replaced 93년생 among young people.
I have no idea who started to use the word first, but I am pretty sure this expression derived from 경규라인, 재석라인, and 호동라인, etc.