It’s just a distribution mechanism that users like. The page details other ways to install, including native methods. The container is at the top just because it will be the first thing many people will want to try.
I don't think I've ever liked the experience of running Docker commands; I think its benefit is the sandboxed environment so the developer has fewer platform variables they need to worry about. I think flatpak is a more user friendly distribution mechanism. But, again, sandboxing really shouldn't be necessary with a Rust TUI application; there really shouldn't be much in the way of platform-specific code in there except maybe the ncurses library