Narrative archetypes (e.g., Hero's Journey, Three-act structure) provide universal story structures that resonate across cultures and media and are important for video game storytelling, yet existing LLM-based methods lack explicit use of these archetypes in procedurally generated games. We propose Forking Garden, a framework for narrative arc-conditioned gameplay planning that generates branching games from user-provided storylines. Our approach first generates a diverse pool of independent nodes, then assembles them into a dungeon graph via arc-guided constraint algorithms, where each node achieves multimodal alignment of gameplay elements. We develop an end-to-end interactive system that instantiates the framework.