The advent of artificial intelligence has propelled AI-Generated Game Commentary (AI-GGC) into a rapidly expanding field, offering benefits such as unlimited availability and personalized narration. However, current researches in this area remain fragmented, and a comprehensive survey that systematically unifies existing efforts is still missing. To bridge this gap, our survey introduces a unified framework that systematically organizes the AI-GGC landscape. We present a novel taxonomy focused on three core commentator capabilities: Live Observation, Strategic Analysis, and Historical Recall. Commentary is further categorized into three functional types: Descriptive, Analytical, and Background. Building on this structure, we provide an in-depth review of state-of-the-art methods, datasets, and evaluation metrics across various game genres. Finally, we highlight key challenges such as real-time reasoning, multimodal integration, and evaluation bottlenecks, and outline promising directions for future research and system development in AI-GGC.