The advent of artificial intelligence has propelled AI-Generated Game Commentary (AI-GGC) into a rapidly expanding research area, offering advantages such as scalable availability and personalized narration. However, existing studies remain fragmented, and a systematic survey that unifies prior efforts is still lacking. 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, and further categorize commentary into three corresponding types: Descriptive Commentary, Analytical Commentary, and Background Commentary. Building on this structure, we provide an in-depth review of methods, datasets, and evaluation metrics, analyzing their strengths and limitations. Finally, we highlight key challenges and point out promising directions for future research in AI-GGC.