Providing individualized support in introductory programming is challenging for teachers in secondary classrooms. Although LLMs can effectively deliver automated feedback in this context, they may provide excessive assistance that hinders learning and lack access to the full context of exploratory environments such as serious games. This study investigates the impact of integrating a pedagogically driven LLM-based digital assistant, which integrates distinct constructivist constraints, into Pyrates, a Python programming game for high schools. In a field user study (N = 241), we found that the assistant was positively perceived by students, supported in-game progression, and significantly reduced teacher interventions without negatively affecting learning. Interaction trace analyses revealed distinct post-feedback strategies, advocating for a tight control of LLM content generation. These findings highlight the feasibility and value of embedding pedagogical principles into LLMs to reduce teacher workload while influencing student strategies and maintaining their learning outcomes in authentic K-12 programming courses.