This study explores and evaluates prompt engineering techniques in game development using Large Language Models (LLMs). As LLMs become increasingly prevalent in technical domains, constructing effective prompts is crucial for generating high-quality game code. Through a series of progressively complex prompts, this study assessed how different prompt structures influence the quality of games generated by Claude and ChatGPT. The findings demonstrate a strong positive correlation between prompt complexity and game quality, with Claude showing significantly higher responsiveness to detailed specifications compared to ChatGPT. A comprehensive evaluation framework is designed using five criteria: Start Interface, Game Interface, Playability, Rhythm Integration, and Game Completeness, providing a standardized method for assessing AI-generated games. The research reveals that prompts incorporating clear technical requirements, gameplay mechanics specifications, and user experience considerations yield optimal results. However, diminishing returns were observed at extreme levels of prompt complexity, suggesting an ideal balance between detail and conciseness. These insights contribute to the understanding of effective LLM utilization in creative technical fields and establish a foundation for future research exploring prompt engineering across various game genres and frameworks as LLM capabilities continue to advance.