Large Language Models (LLMs) enable dynamic game interactions but fail to follow essential procedural flows in rule-governed trading systems, eroding player trust. This work resolves the core tension between the creative flexibility of LLMs and the procedural demands of in-game trading (browse-offer-review-confirm). To this end, Autoregressive State-Tracking Prompting (ASTP) is introduced, a methodology centered on a strategically orchestrated prompt that compels an LLM to make its state-tracking process explicit and verifiable. Instead of relying on implicit contextual understanding, ASTP tasks the LLM with identifying and reporting a predefined state label from the previous turn. To ensure transactional integrity, this is complemented by a state-specific placeholder post-processing method for accurate price calculations. Evaluation across 300 trading dialogues demonstrates >99% state compliance and 99.3% calculation precision. Notably, ASTP with placeholder post-processing on smaller models (Gemini-2.5-Flash) matches larger models' (Gemini-2.5-Pro) performance while reducing response time from 21.2s to 2.4s, establishing a practical foundation that satisfies both real-time requirements and resource constraints of commercial games.