Deleting your account removes it and everything stored with it: your nickname, rating, rank, game history, friend code, any linked Google or Apple identifier, and your chat block list. This cannot be undone.
If you no longer have your device, email support@shogicastle.com from any address and include your friend code (shown on your profile in the app). We delete the account within 7 days and reply when it is done. Without the friend code we cannot find the account, because we hold no email, name or other identifier for it.
Everything that never left your phone (settings, puzzle progress, offline games) is removed simply by uninstalling the app.
Nothing that identifies you. Aggregate statistics, such as how many games were played on a given day, are not tied to any account and are unaffected.