Short videos have quickly taken over the mobile screens of network users and established themselves as one of the most significant social platforms in the “Internet+era” as a new carrier of social culture. Short films have the qualities of high participation, strong engagement, high real-time, and quick propagation, which satisfy the needs of Internet users in interpersonal communication and reading or enjoyment in leisure time. This is against the backdrop of network big data environment monitoring. Based on this, the paper defines the fair use system of short video copyright, elaborates on its concept, examines the system’s challenges and potential fixes in the context of networks, and develops a model for short video repeat detection using local key points. According to the experimental findings, this algorithm’s short video repetition detection accuracy rate can reach 95.8%, and its recall rate can reach 94.5%. For the development of the fair use system of short video copyright in the current network environment, the video in some complex scenes can achieve good detection performance, which establishes a good data analysis foundation and provides a significant amount of assistance for the system to escape its predicament.