Looking at the pdf folder, this is the "Multitasking MS-DOS" product which is not the same as the "DOS 4" that most people think of. That "DOS 4" is actually IBM Personal Computer DOS 4, the successor to MS-DOS/PC-DOS 3.3 (with > 32 meg filesystem support borrowed from Compaq DOS 3.31) and predecessor to MS-DOS 5. Microsoft did later, quite confusingly, also release an MS-DOS 4 based on PC-DOS 4.
This is not that. This is the road not taken, at least not by IBM and compatibles.
At the time, Microsoft assumed that DOS as we know it would never live past version 3. This was their idea of what DOS 4 should be. A new major version breaking strict compatibility. What we know as OS/2 1.x was originally named DOS 5, another new major "DOS" version breaking strict compatibility.
This Multitasking MS-DOS never took off except in niche applications, and OS/2 eventually got its own product name which is why there were then regular DOS releases 4 and 5 followed by 6 and eventually 7 become part of Windows 95.
It’s hard to tell. According to Wikipedia, DOS 4.0 is different than 4.00
> MS-DOS 4.0 (multitasking) and MS-DOS 4.1 – A separate branch of development with additional multitasking features, released between 3.2 and 3.3, and later abandoned. It is unrelated to any later versions, including versions 4.00 and 4.01 listed below