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.
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.
It looks like a fun project.