It's not its own kernel, but emacs can run on Linux as PID 1, at which point it rather seems like it should count as an OS. Given its affiliation, emacs/Linux probably still counts as GNU/Linux, but still...
PID 1 has some unique responsibilities. In particular, any process that gets orphaned when its original parent exits is automatically reparented by PID 1, and so the process running as PID 1 must watch for unexpected SIGCHILD and clean up the zombies with waitpid or similar.
One could argue (many have, in the form of a tedious copypasta) that Linux is not the operating system because an operating system needs both a kernel and a userland.
Why wouldn't `nano` count as a userland in the same way as anything provided by a typical distro today?
Well, cat and echo can't run other programs, so no they wouldn't qualify. I'd have to check the nano docs to see if it can spawn other programs, but I'd be shocked if it's any good at it. In stark contrast, emacs can and is good at running programs, including interactively in terminals that it manages itself. I'm happy to agree that the kernel is a big part of the OS, but a kernel alone does not an OS make.
What we do know is that the S in OS stands for system. A kernel alone does not a system make. There needs to be other components to round out an entire system. Why does Emacs not fit the bill?