Refers to the person who finishes second or just behind the winner in a competition, election, or ranking.
He became the runner-up in the election.
The runner-up was also given a prize.
次点 is the abstract 'second place' or 'next highest score', while 次点者 specifically refers to the person holding that position.
Compound of 次点 (second place, next highest score) + 者 (person).