Movie scripts pose a fundamental challenge for automatic summarization due to their non-linear, cross-cut narrative structure, which makes surface-level saliency methods ineffective at preserving core story progression. To address this, we introduce S^2tory (Story Spine Distillation), a narratology-grounded framework that leverages character development trajectories to identify plot nuclei, the essential events that drive the narrative forward, while filtering out peripheral satellite events that merely enrich atmosphere or emotion. Our Narrative Expert Agent (NEAgent) performs theory-constrained reasoning, whose distilled knowledge conditions a small model to identify plot nuclei. Another model then uses these plot nuclei to generate the summary. Experiments on the MovieSum dataset demonstrate state-of-the-art semantic fidelity at approximately 3.5x compression, and zero-shot evaluation on BookSum confirms strong out-of-domain generalization. Human evaluation further validates that narratological theory provides an indispensable foundation for modeling complex, non-linear narratives.