Facebook lost my account that I used for an iOS game, is there any way to hack the login to retrieve my account back?
You’re at a dead end of the developers won’t release your account tied to validating against Facebook identity. 

Unless they have a save file, you wouldn’t be able to reverse engineer it and would have to crack into Facebook or replicate their entire validation system and fool the app to thinking it’s talking to Facebook and is instead talking to your web application and API and you also get past the encryption the developer put in their app to check certificates. 

This is all doable, but needs quite advanced skills. For a game, not worth the effort. For a career in security, this would make an excellent paper or project and could get you hired. 

Just because your Facebook data is deleted, you could still recover and reactivate the account. I would start to get the account back if you can - https://www.facebook.com/login/identify/