The fact that Handbrake doesn't expose the same features as the ffmpeg CLI tool is frankly irrelevant.It's not just relevant, it's the whole thing. They asked for an ffmpeg GUI and someone recommended a GUI that doesn't use ffmpeg and doesn't do what ffmpeg can do. ffmpeg can not only rewire channels, it can stream video, capture video from the screen, capture video from a tv tuner, overlay text etc.
Also the libraries you listed are part of the ffmpeg project. They come from ffmpeg.
https://ffmpeg.org/about.html
Also they asked for a GUI to ffmpeg, not necessarily a GUI to the command line tool.