I think this feature came out some months ago, but personally didn't see any games with a sub-game. What do they mean, and on which cases you should add a sub-game instead of requesting a new one?

Perhaps like a DLC of a game that includes a whole new storyline and is seperate from the main story?

Ape escape 2 and Ape escape 3 have sun games and might be examples to look at.

Both games have mini games in them that you can unlock, and have separate leader boards

Celeste uses subgames for custom maps I think

Thanks for the answers. Another question, is a sub-game need to be requested (like normal games), or it can be added by the game moderators?

If you don't have a series to your game, via the normal ways. Do state in the request that it's a sub-game of game X, so that the person accepting game requests knows what to do.