The App Store is the graphical package manager interface. Or in the case of apps that haven't published, the Finder/Applications folder itself. It makes a lot of sense, similar to the way GoboLinux stashed packages in its new world filesystem hierarchy. One folder, one package.
You do not need a new filesystem hierarchy for it. I have a "one folder one package" kind of setup (among others), e.g. packages are at ~/.local/pkg and I have them symlinked from there to ~/.local. It works for many programs. I use "zpkg", but you could use "GNU stow", too.
You download a DMG file or something, then you drag and drop some icon into your “applications” folder
It is kind of dumb. I haven’t seen any graphical package manage interface to handle this.