The last thing the world needs is another Linux package manager. F-Droid uses apt and it could hardly be considered Debian.
It's an interesting question though, that I haven't thought about. At a minimum I'd say that it should have some sort of coherent goals and philosophy, its own package repository, and should not be replicable from its parent distro with a script to install/remove various packages.
The last one is probably the most critical, if it can do something the base distro can't, then it at least has a reason to exist, whether or not you want to call it a "distro" or not.