Developing 3D games requires specialized expertise across multiple domains, including programming, 3D modeling, and engine configuration, which limits access to millions of potential creators. Recently, researchers have begun to explore automated game development. However, existing approaches face three primary challenges: (1) limited scope to 2D content generation or isolated code snippets; (2) requirement for manual integration of generated components into game engines; and (3) poor performance on handling interactive game logic and state management. While Multimodal Large Language Models (MLLMs) demonstrate potential capabilities to ease the game generation task, a critical gap still remains in translating these outputs into production-ready, executable game projects based on game engines such as Unity and Unreal Engine. To bridge the gap, this paper introduces UniGen, the first end-to-end coordinated multi-agent framework that automates zero-coding development of runnable 3D games from natural language requirements. Specifically, UniGen uses a Planning Agent that interprets user requirements into structured blueprints and engineered logic descriptions; after which a Generation Agent produces executable C# scripts; then an Automation Agent handles engine-specific component binding and scene construction; and lastly a Debugging Agent provides real-time error correction through conversational interaction. We evaluated UniGen on three distinct game prototypes. Results demonstrate that UniGen not only democratizes game creation by requiring no coding from the user, but also reduces development time by 91.4%. We release UniGen at https://github.com/yxwan123/UniGen. A video demonstration is available at https://www.youtube.com/watch?v=xyJjFfnxUx0.