Providing video streaming for unmanned systems has the potential to facilitate various applications. However, in remote areas, providing communication services through ground networks is challenging due to high construction costs. Using satellites for video services can address issues such as limited ground network coverage, poor disaster resistance, and difficulty in dealing with special terrains and emergencies. However, satellite communication networks are confront with challenges such as limited energy, restricted frequency and time resources, and time-varying satellite-to-ground links, which have significant impacts on the transmission of video data. This work studies the optimization of Scalable Video Streaming (SVC) downlink transmission for multiple unmanned systems through satellite relays. The paper uses Lyapunov stochastic optimization theory to decompose the original problem into three independent sub-problems: satellite power allocation, SVC video layer selection, and time resource allocation. Then, separate solutions are proposed for the sub-problems and are summarized into an algorithm for optimizing video transmission. Experimental results demonstrate that the proposed algorithm outperforms existing algorithms in enhancing video quality, reducing interruption rates, and increasing overall system throughput, significantly improving the unmanned system performance.