I tried writing a simple OS decades ago as an EXE you'd run from MSDOS. It would rewrite all the ISR vectors and take over all the memory including the space that was previously used by MSDOS. I was told that because I relied on DOS, whatever I wrote was not an operating system. I politely disagreed.
LOADLIN could load linux from DOS. And being a .EXE it relied on DOS to bootstrap.
So yes, if you didn't use the DOS code (I mean… you overwrote it), then DOS is not there. And if DOS is not the OS, that just leaves your code to be the OS. :-)
See also both Windows 3.1 and the “DOS extenders” used to build applications that were launched from DOS but ran in protected mode with additional facilities.
