Human manipulation videos provide rich motion and interaction cues for acquiring robot skills without robot demonstrations. Video generation models synthesize such demonstrations from an initial scene image and task instruction, avoiding the need to record demonstrations for each task. However, the recovered motion captures only one scene-specific realization, leaving task structure, geometric relations, and constraints implicit. We present V2-STRep, a zero-shot framework that converts generated video motion into reusable robot skills through VLM-grounded structured task representations. The representation specifies motion phases, references, and task-relevant constraints, with targets described by minimal geometric structures: points, point-normals, axes, planes, and full 6D poses. VLM-provided 2D image-space cues are lifted into 3D using RGB-D observations to reconstruct task geometry and candidate grasp poses. Geometry-specific rules transfer motion to new scenes, while task-constrained trajectory optimization couples grasp selection with complete robot motion planning. It preserves task requirements while using remaining rotational freedom to accommodate joint limits. Updating deployment grounding and constraints enables reuse under new compatible instructions without generating another video. Experiments on six real-world manipulation tasks demonstrate improved execution success over baselines, reliable cross-scene transfer of successfully acquired skills, and adaptation to changed deployment instructions. Details are available on the project website: https://tuwien-asl.github.io/V2-STRep/.

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