I'm not sure what Apple can do about it. It's 100% up to the developer.
Apple provide an authentication mechanism that developers can use to identify users rather than (or in addition to) maintaining their own username/password authentication scheme.
To do that, you log in with your Apple Account and Apple provides the applications with a token used for future authentication.
You deleting your Apple Account with the app means the developer throws away the token and they no longer have a way to associate your account with your Apple Account.
In theory, they should still have an account for you, and they would be remiss if they only had one way of identifying you (e.g. via Apple Account). If they really do, then the account is likely lost, however, they would be the ones to answer the question as to what other authentication options are available.