Part two of the tutorial on building a multiplayer tic-tac-toe game with React Native and PubNub focuses on implementing the core game functionality, including the game component, UI setup, and logic for gameplay. The tutorial details creating the game board and functionality to track player moves, check for winning conditions, and update scores. It explains how to handle player turns and integrate real-time updates using PubNub. The tutorial also covers setting up a channel listener for game updates and managing game state changes, like starting a new game or ending the session. Testing the app involves using simulators and a React test app to simulate real-world gameplay scenarios. The tutorial concludes by directing users to additional resources for integrating PubNub with React applications and provides information on exploring further PubNub capabilities for enhancing React projects.