Hyperspectral 3D imaging captures both depth maps and hyperspectral images, enabling comprehensive geometric and material analysis. Recent methods achieve high spectral and depth accuracy; however, they require long acquisition times often over several minutes or rely on large, expensive systems, restricting their use to static scenes. We present Dense Dispersed Structured Light (DDSL), an accurate hyperspectral 3D imaging method for dynamic scenes that utilizes stereo RGB cameras and an RGB projector equipped with an affordable diffraction grating film. We design spectrally multiplexed DDSL patterns that significantly reduce the number of required projector patterns, thereby accelerating acquisition speed. Additionally, we formulate an image formation model and a reconstruction method to estimate a hyperspectral image and depth map from captured stereo images. As the first practical and accurate hyperspectral 3D imaging method for dynamic scenes, we experimentally demonstrate that DDSL achieves a spectral resolution of 15.5 nm full width at half maximum (FWHM), a depth error of 4 mm, and a frame rate of 6.6 fps.