3D Gaussian Splatting (3DGS) has witnessed its rapid development in novel view synthesis, which attains high quality reconstruction and real-time rendering. At the same time, there is still a gap before implicit neural representation (INR) can become a practical compressor due to the lack of stream decoding and real-time frame reconstruction on consumer-grade hardware. It remains a question whether the fast rendering and partial parameter decoding characteristics of 3DGS are applicable to video compression. To address these challenges, we propose a Toast-like Sliding Window (TSW) orthographic projection for converting any 3D Gaussian model into a video representation model. This method efficiently represents video by leveraging temporal redundancy through a sliding window approach. Additionally, the converted model is inherently stream-decodable and offers a higher rendering frame rate compared to INR methods. Building on TSW, we introduce an end-to-end trainable video compression method, GSVC, which employs deformable Gaussian representation and optical flow guidance to capture dynamic content in videos. Experimental results demonstrate that our method effectively transforms a 3D Gaussian model into a practical video compressor. GSVC further achieves better rate-distortion performance than NeRV on the UVG dataset, while achieving higher frame reconstruction speed (+30%~40% fps) and stream decoding. Code is available at Github