Large language models (LLMs) are increasingly used to support software development, but their practical usefulness in applied game-development settings remains underexplored, especially when generated code must be integrated into an existing game software system. This paper presents an exploratory empirical case study of GPT-4o in a custom Python/Pygame endless runner. The study examines six selected development tasks: three localized refactoring tasks and three tasks involving gameplay feature generation. The resulting implementations were evaluated using software metrics, unit tests, and manual gameplay assessments. In this case study, all three selected refactoring tasks were completed successfully in functional terms, whereas only one of the three selected gameplay feature generation tasks resulted in a correctly integrated feature. The findings suggest that, in this setting, GPT-4o handled localized transformations more reliably than tasks requiring new gameplay interactions across multiple existing systems. Given the exploratory single-case design, these results are best interpreted as indicative observations rather than as generalizable evidence of category-level model performance. Overall, the paper contributes a transparent case-based account of the opportunities and limitations of LLM-assisted refactoring and gameplay feature generation in an existing game software system.