The development of Artificial Intelligence (AI) enables humans to co-create content with machines. The unexpectedness of AI-generated content can bring inspiration and entertainment to users. However, the co-creation interactions are always designed for content creators and have poor accessibility. To explore gamification of mixed-initiative co-creation and make human-AI interactions accessible and fun for players, I prototyped Snake Story, a mixed-initiative game where players can select AI-generated texts to write a story of a snake by playing a "Snake" like game. A controlled experiment was conducted to investigate the dynamics of player-AI interactions with and without the game component in the designed interface. As a result of a study with 11 players (n=11), I found that players utilized different strategies when playing with the two versions, game mechanics significantly affected the output stories, players' creative process, as well as role perceptions, and players with different backgrounds showed different preferences for the two versions. Based on these results, I further discussed considerations for mixed-initiative game design. This work aims to inspire the design of engaging co-creation experiences.