Traditional approaches -- such as Win Probability Added (WPA)-based ranking or computer vision-driven event detection -- can identify scoring plays but often miss strategic depth, momentum shifts, and storyline progression. Manual curation remains the gold standard but is resource-intensive and not scalable. We introduce DIAMOND, an LLM-driven agent for context-aware baseball highlight summarization that integrates structured sports analytics with natural language reasoning. DIAMOND leverages sabermetric features -- Win Expectancy, WPA, and Leverage Index -- to quantify play importance, while an LLM module enhances selection based on contextual narrative value. This hybrid approach ensures both quantitative rigor and qualitative richness, surpassing the limitations of purely statistical or vision-based systems. Evaluated on five diverse Korean Baseball Organization League games, DIAMOND improves F1-score from 42.9% (WPA-only) to 84.8%, outperforming both commercial and statistical baselines. Though limited in scale, our results highlight the potential of modular, interpretable agent-based frameworks for event-level summarization in sports and beyond.