Generative Artificial Intelligence (GenAI) tools are transforming creative practices, yet their role in game poem design remains largely unexplored. Game poems serve as a bridge between interactive artwork and design for engagement. Although game poems themselves are a small genre, they serve as a microcosm for exploring how AI influences minimal, expressive, and human-centric design. This research was based on ten student-made game poems with GenAI tools. Using qualitative analysis, this study explores how student designers navigate, integrate, and revise GenAI in game poem making. Analysis of the ten included student projects demonstrates that the influence of GenAI accelerates technical implementation and ideation scaffolding, but human authorship and emotional intention play a vital role in game poem design. Students simultaneously engaged in iterative prompting, Human Creative Override, and manual curation to negotiate GenAI’s outputs.