Isn't a specialized "editor" is antithetical to the very idea behind Markdown,
which is to make written text as readable as possible both in plain text and
the web? Markdown syntax is already too simple. The original authors even mention "plain text e-mail" as their
biggest source inspiration. [1]
The text is still readable as plaintext, but I think you could concede that styling it a bit does make it easier to see the effect of your markdown.
It's like how, say, Sublime text has a syntax highlighter for markdown files. Sure, you could argue that is enough to signify that the contained text is bold, but it's hard to deny that also bolding that text in the editing stage is helpful.
Syntax "highlighting" like in OP's editor will always provide more than just plain text formatting can. So it's not really antithetical anyway. Sure, markdown is made to make written text as readable as possible in plain text, but that doesn't mean it can't be even more readable in a non-plain text setting.
No, of course not. While Markdown is plain text, it is a markup language with its own syntax. This syntax is parsed by tools to transform Markdown into other formats. As it happens, this is analogous to code: encoded as text with a specific syntax.
As such, "markdown editors" are for the most part text editors with syntax highlighting. The syntax is important because it encodes the user's intent beyond the raw text bytes. Just as with code editor's highlighters, we use them because it provides an immediate and useful visualization of our intent. "Why isn't my link highlighted? OH, missed that paren." "Why is everything italic? OH, fat-fingered the closing asterisk."
So while well-formatted Markdown happens to also be well-formatted plain-text, but that doesn't mean that good authoring tools aren't needed or helpful.
[1]: https://daringfireball.net/projects/markdown/