You can create multiple leader-board inside AppHQ Management Console, means according to date you can create one leaderboard and save entries into it. It will help you to maintain daily leaderboard in the easy manner. Also, in the month end, you can delete first fifteen days leaderboard from the database.
Note: As of now, we have no such plan to release the deleteGame API. You can delete it through dashboard only.
P.S I am adding your request to our development team to take a look at deleteGame functionality. If it is possible to release the API, then I will update you regarding the release timeline.