Video analysis using artificial intelligence (AI) is widely adopted in various services. However, ground users with limited resources may not process such tasks locally. Fortunately, the ultra-dense low earth orbit (LEO) satellite networks allow multiple satellites to cooperatively handle these tasks to provide low-latency computing services. Therefore, this paper considers a cooperative computation offloading scheme for video analysis in ultra-dense LEO satellite-terrestrial networks, allowing for flexible task scheduling and video quality selection. Considering the privacy of satellites and the dynamic network environment, the cooperative computation offloading problem is established as a distributed Markov decision process (MDP) to reduce the task delay while increasing the accuracy of video analysis. Then, a multi-agent deep reinforcement learning (DRL) approach is proposed to obtain efficient offloading strategies. Finally, simulations are conducted to verify the feasibility and performance of the proposed scheme.