I searched on Google many times and could not find a good and clear documentation or example about how to implement Google Play Leaderboard. Do you have any idea about it?
If you don’t want to eject, it looks like you will need to use the Play Games Services for Web. However, as that page says:
Important: Google Play games services is deprecated for client-only web games, and is not likely to function as expected. Do not use Google Play games services for new client-only web games. Server-side calls to the REST API to service Android games will continue to be supported (see here for more details about server-side REST API access for Android games).
This means you need to create a web service that talks to the Leaderboard using the above REST API and then your app can talk to your web service.
If you don’t mind ejecting, this project looks like it should work for you.