Mux Video aims to change the abstraction level for video handling in software development by allowing developers to build directly around the concept of video rather than managing files, asynchronous jobs, and other complexities. This higher-level abstraction simplifies the process of building software that works with video, making it more efficient and practical for companies not named YouTube, Netflix, or Facebook. Mux Video's API abstracts away the complexity of handling video, allowing developers to focus on creating their own software and improving user experience.