Scientific knowledge is often abstract and challenging, making it difficult for students to apply these concepts effectively. Digital game-based learning (DGBL) offers an engaging and immersive approach, but the fixed resources and predetermined learning paths in most games limit its ability to adapt to individual learners' needs. Large language models, as advanced conversational agents, are capable of personalized interaction by adapting to users' language styles, interests, and preferences. This study explores a large language model-based adaptive contextual game (LLM-ACG) approach aimed at transforming scientific education into engaging, interactive, and supportive learning environments. Additionally, this research examines the impacts of the LLM-ACG approach on academic performance, flow experiences, cognitive load, and behavioral patterns among students. A quasi-experimental design was employed to compare the differences in academic achievements and flow experiences between the LLM-ACG approach and the conventional contextual game (C-CG) approach among fifth-grade students. Furthermore, an in-depth analysis of student behavioral patterns during gameplay was conducted through lagged sequence analysis. The findings indicate that the LLM-ACG approach demonstrates a clear advantage over C-CG in terms of enhancing students' academic achievements and flow experiences. It effectively reduces cognitive load and significantly promotes positive learning behaviors and sustained motivation among students.