I don’t understand: what makes this “DOS-like”? Not even the command names match DOS, except for dir and cls, and the architecture and feature set are completely different.
Ultimately, it's an eye of the beholder type thing, but it seems very fair to call it DOS-like to me. The DOS inspiration is pretty blatant all throughout it from its aesthetic, commands (more than just dir and cls is shared), booting from a 1.44 floppy, etc. And if you are coming from a primarily windows computing background, then "DOS-like" is entirely appropriate to me.
You are right, it goes way ahead the first iteration. I call it DOS-like because of its resemblance to the Text mode-only operating systems (and to MS-DOS especially). On the other hand, it shares very little as the architecture, command set, or hardware utilization approach are concerned when compared to MS-DOS.