The rules say: "All games must include a leaderboard system (offline or online) so that the players can compete for a high score if they happen to win the contest."
So a simple offline leaderboard should suffice, just store names and scores in an array or object and save it in local storage or something.
Although I can also recommend using Microsoft Azure PlayFab, it gives you a fairly easy way to implement an online leaderboard especially if you're using Unity. I implemented an online leaderboard last weekend in a Construct 3 game following this tutorial, it took me about an hour.
