It wasn't anything like WSL. WSL runs Linux programs under a different kernel by replicating the syscall interface. This was basically a bootloader (loadlin) and a filesystem driver (umsdos). This was a very different world because DOS was hardly an operating system at all, it was just this tiny thing that installed itself into some interrupt handlers right after BIOS. Loadlin could take over and load a full linux kernel, no different from how grub works today (or LILO before that).
Yes, DOS was basically a boot loader and utilities. The EFI shell is modeled the same way, though DOS had fewer address bits available. Netware also used it in this fashion, as a boot loader that may/not initialize hardware.
From memory, the next stage of the OS would simply write itself over DOS in memory, move the instruction pointer and go.
