I noticed that, while most platforms have their exclusive tag, MS-DOS games share a tag with non-MS-DOS games that just look like MS-DOS.

I like to download MS-DOS games and play them in my 386, and it's very frustrating to see an appealing "MS-DOS" game only to discover that it's a game for modern Windows systems that just looks like an MS-DOS game. At least, I can tell before downloading because of the ridiculous size of the download file... But when I browse MS-DOS games, I want to see only games that will work on actual MS-DOS.

Can a new tag be created that only includes real MS-DOS games??

Yes, you can create any tags you want. The challenge is getting other creators to use it.

that only includes real MS-DOS games

No. There is no strict tag enforcement. 

Games in https://itch.io/games/tag-ms-dos and https://itch.io/games/tag-dos do not promise that they run under a specific version of any DOS.

A tag only means that the game has something to do with the tag. So even games that just look like a DOS game might use it.

The operating system meta tags do not even include the OS version. It just says Windows. Which Windows? Windows 3.11?

In theory, you could try to establish a tag that means, that a game has a version that will run under a specific 30 year old DOS version. But as no time pointed out, the challenge is, to convinve other people to use it.

If the download file is big, maybe there is freedos included. Or, it's just a game simulating the dos style, but the description should tell you more. 

And if you missed it, tags are not created by Itch. The list of tags you see, is just the "suggested" tags, which basically is self referencing, since it just means, the tags are in that list. There is https://itch.io/games/tag-386 and https://itch.io/games/tag-486 , but only a handful of games use it.

Some of the "DOS" games with Windows downloads are actual DOS games packaged with a Windows version of DOSBox.

I agree that situation sucks for minority platforms like DOS (and Amiga and C64 and Spectrum and NES and so on).   Ideally they would all be treated as first-class platforms instead of relying on tags.