Regarding CryptoKitties, it is not possible to do in the same way as it is done on Ethereum, but it can be done using a process called 'soft consensus'. It is what SteemMonsters uses, and is explained here: https://steemit.com/steem/@steemitblog/steemit-interviews-steemmonsters.
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I had read that interview when it was first published, but I had mostly just sort of skimmed it. I read it carefully just now and I'm still not quite sure how they use soft consensus...but while reading it I did kind of have some ideas on how you might be able to do a fully distributed app on the Steem blockchain.
The only way I can really think of possibly doing it is by having people run software on servers and their home computers to validate "transactions" and then pay them with proceeds from the game for their services. That would sort of lose some of the benefits of Steem, but you have to pay for servers. So, rather than running servers yourself, you would have a sort of smart contract that pays people for running servers for the app.
Perhaps you know of some other resources to read on this? I'm going to be doing a deep dive into it for the next few months, as I would like to eventually figure out how to do some kind of blockchain based games and apps. Even if I never end up making anything successful, learning's fun.
There are also extreme benefits of figuring out how to do this on Steem. Plus, I like Steem.
The basic idea behind soft-consensus is that a set of rules are written for how to interpret the data on the blockchain, and the application follows those rules. The blockchain itself will not reject blocks with "bad data" (that doesn't follow the rules), but the application layer will. It is 100% publicly auditable, since the data is all in the blockchain.