The evolution of semantic communications has profoundly impacted wireless video transmission, whose applications dominate driver of modern bandwidth consumption. However, most existing schemes are predominantly optimized for simple additive white Gaussian noise or Rayleigh fading channels, neglecting the ubiquitous multiple-input multiple-output (MIMO) environments that critically hinder practical deployment. To bridge this gap, we propose the context video semantic transmission (CVST) framework under MIMO channels. Building upon an efficient contextual video transmission backbone, CVST effectively learns a context-channel correlation map to explicitly formulate the relationships between feature groups and MIMO subchannels. Leveraging these channel-aware features, we design a multi-reference entropy coding mechanism, enabling channel state-aware variable length coding. Furthermore, CVST incorporates a checkerboard-based feature modulation strategy to achieve multiple rate points within a single trained model, thereby enhancing deployment flexibility. These innovations constitute our multi-reference variable length and rate coding (MR-VLRC) scheme. By integrating contextual transmission with MR-VLRC, CVST demonstrates substantial performance gains over various standardized separated coding methods and recent wireless video semantic communication approaches. The code is available at https://github.com/xie233333/CVST.