It is a good idea to make most of the calculations and fights offchain to avoid overloading of the main network.

Things like who owns what creature will be tokenized usring ERC721. That sounds like a common practice now.

Things like experience on different servers, fight logs, overall activity log, stats and skill sets will stay offchain too. Most of them will be recently updated and it does not make sense to spend Ether on that. We might choose fork of EOS or any other blockchain for instance to store some of those value in the future. However while the game process with be identified, adjusted and discussed with the community it makes sense to keep it on the servers.

If there are any other propositions lets discuss them.