Large Language Models' capacity to reason in natural language makes them uniquely promising for 4X and grand strategy games, enabling more natural human-AI gameplay interactions such as collaboration and negotiation. However, these games present unique challenges due to their complexity and long-horizon nature, while latency and cost factors may hinder LLMs' real-world deployment. Working on a classic 4X strategy game, Sid Meier's Civilization V with the Vox Populi mod, we introduce Vox Deorum, a hybrid LLM+X architecture. Our layered technical design empowers LLMs to handle macro-strategic reasoning, delegating tactical execution to subsystems (e.g., algorithmic AI or reinforcement learning AI in the future). We validate our approach through 2,327 complete games, comparing two open-source LLMs with a simple prompt against Vox Populi's enhanced AI. Results show that LLMs achieve competitive end-to-end gameplay while exhibiting play styles that diverge substantially from algorithmic AI and from each other. Our work establishes a viable architecture for integrating LLMs in commercial 4X games, opening new opportunities for game design and agentic AI research.