It's very interesting - each cat in the game is completely unique. Technically - each cat is a ERC721 token, i.e. non-fungible asset, that you can hold on your wallet or sell it on DEXes, whenever you want. You can set your own price on that token. Sometimes people just set crazy prices for their kitties expecting some wild buyer smh.
CryptoKitties was created to demonstrate the use-case of Decentralized ownership and tokenizing assets in the internet. And with the hint, that you can do the same thing in REAL LIFE. It's showing us that Ethereum blockchain could be very useful for this purpose.
Each ERC721 token can have its own unique attributes, which cannot be used for other tokens in the same way. If you bought a specific token (e.g. crypto-cat) - it's completely yours and no one can take it from you, as long as you hold the private key of your wallet.