The game industry, now generating over $200 billion annually, has become a major force in entertainment, yet game development remains underexplored in software engineering research. Generative AI (GenAI) has introduced new opportunities for content automation in game development, offering benefits in testing, design, and player engagement. However, integrating GenAI across game development phases presents unique technical, creative, and collaborative challenges. This study aims to develop an adaptable framework that addresses these challenges by providing practical insights and strategies to enhance collaboration, creativity, and efficiency. Using a mixed-methods approach, including open-source analysis and developer surveys and interviews, we will construct a grounded theory on GenAI adoption. The insights will inform a framework refined with industry feedback, contributing datasets, guidelines, and tools to support sustainable GenAI integration in game development.