This paper proposes Memory-Augmented State Machine Prompting (MASMP), a novel framework for LLM agents in real-time strategy games. Addressing key challenges like hallucinations and fragmented decision-making in existing approaches, MASMP integrates state machine prompting with memory mechanisms to unify structured actions with long-term tactical coherence. The framework features: (1) a natural language-driven state machine architecture that guides LLMs to emulate finite state machines and behavior trees through prompts, and (2) a lightweight memory module preserving strategic variables (e.g., tactics, priority units) across decision cycles. Experiments in StarCraft II demonstrate MASMP's 60% win rate against the hardest built-in AI (Lv7), vastly outperforming baselines (0%). Case studies reveal the method retains LLMs' semantic comprehension while resolving the "Knowing-Doing Gap" through strict state-action mapping, achieving both interpretability and FSM-like reliability. This work establishes a new paradigm for combining neural and symbolic AI in complex decision-making.