DOS had no kernel - it was just a bunch of code that ran on top of a bunch of PC-compatible hardware. There was no separation between kernel-space and user-space.
You are applying an overly restrictive definition to something that is just the nut analogy, which is a vague analogy that does not imply "spaces".
MS/PC-DOS, and DR-DOS, were not just "a bunch of code" and had a definite structure when it came to operating system design. They comprised the basic disc operating system, the basic input/output system (incorporating built-in and loadable device drivers), the command processor, and the housekeeping utilities.
The kernel of (386 Enhanced Mode) DOS+Windows analogous to the Windows NT kernel being discussed here is the VMM and the VxDs, with krnl386.exe as a distinguished Extended DOS program running in the distinguished system VM.
