Off-Chain - Utilizing a traditional database or application layer for an application's heavy lifting. There is nothing wrong with utilizing a database for what it's meant to do, and helps to keep only components of an application that can truly benefit from being decentralized on-chain.
On-Chain - Relying on what blockchains are good at now, on-chain components of an application could very well just focus on payments, ownership of digital assets, game assets bought with cryptocurrency, and authorization/verification that you indeed bought x item to interact with smart contracts that are part of application.
Game settings, design algorithms (i.e the GeneScience or KittyAccessControl code in CryptoKitties), admin aspects, pricing models, should be done off-chain if utilizing something like OPEN.
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Thank you for the explanation! Definitely will look into this more.