For all the bad rap it got (some of which was deserved), ME bypassed real-mode MS-DOS (and its config files) at bootup, and loaded its own protected-mode drivers, etc. in IO.SYS. It also loaded the main registry hive only once, and parallelized PnP resolution, significantly improving boot-up time. It also incorporated Windows 2000's networking stack, and added support for UPnP.
In many ways, ME was a stepping stone, getting some users on less-capable hardware onto Windows 2000 class OS features, without requiring a complete hardware upgrade.
Everyone's favorite error message: the Microsoft Installable File System Manager cannot find the helper driver. Please ensure that IFSHLP.SYS has been installed.
This means Windows ME needs a real mode DOS helper for certain file system operations.
I can't remember whether the INT 21h function 55h (Create PSP) was still called as frequently as in earlier Windows and handled in DOS but I betcha.
Its job was to provide 32-bit file access (bypassing 16-bit DOS file IO mechanisms), and ensuring nothing else on the system could intercept INT 21h calls.
ME didn't depend on MS-DOS (though it did provide support for running MS-DOS apps).