They ship a custom kernel, have their own packaging servers, ship their own installer, an installable ISO, and ship a bunch of custom UI. That's a distro, all right. Not a foundational one a la Debian or Arch, but that's never been a requirement seeing how things like Ubuntu, Cachy etc. exist and are called distros without issue.

Omarchy started as a pile of dotfiles a year ago. It isn't that anymore, and DHH's intended direction is towards a fully independent foundation distro.