As per a company specializing in Android App Development Company in USA, in order to design a DApp game similar to CryptoKitties:

Understand the Blockchain Technology: Start by gaining a deep understanding of blockchain technology, especially Ethereum, which is commonly used for DApp development. Understanding smart contracts and how they interact with the blockchain is crucial.

Design Unique In-Game Assets: Design and develop unique in-game assets, such as digital collectible items (in this case, digital cats), and assign them specific attributes or features. These assets will be stored as non-fungible tokens (NFTs) on the blockchain.

Smart Contract Development: Hire blockchain developers or collaborate with experts to create the smart contracts that govern the creation, ownership, and transfer of these NFTs. These contracts define the rules of your game and interactions between players.

Front-End Development: Develop a user-friendly front-end interface for the game where players can interact with the DApp, buy, sell, and breed their digital assets (CryptoKitties). Ensure that it connects seamlessly with the blockchain through APIs.

Security and Scalability: Security is paramount in blockchain-based games. Implement security measures to protect user data and assets. Consider scalability solutions to handle an increasing number of players and transactions efficiently.

Market and Community Building: Promote your DApp game through various marketing channels, engage with the blockchain community, and create a marketplace for players to buy, sell, and trade their digital assets. Building a strong user community is essential for the success of your DApp game like CryptoKitties.