The article actually fails to answer the question in the title. It's a long list of reasons the author believes it should not be popular. But it clearly is massively popular. So maybe there's something wrong with his line of reasoning?

Anyway, Markdown emerged out of the Ruby community. So it's not strange that there is no specification. Ruby is a dynamically typed language so, ruby programmers tend to not specify a lot of things like types or schemas. And indeed the Ruby language it self is a bit under-specified. The spec is simply "whatever ruby does is what it does", which sucks for alternate implementations like JRuby. The same is true for Markdown. Whatever the original markdown library does was the spec. And it has since been loosely implemented by others doing their own Markdown derivatives. Like the widely used Github flavor. Which is also a ruby based implementation, I think. So it is similarly under specified.

However, the lack of a specification is not much of an issue since markdown is used by humans to be turned into something human readable with some html formatting. Either it's readable or you fix it. And it's simple enough that any markup typos in markdown are usually not that big of a deal. The main goal of Markdown is to get out of the user's way so they can focus on content rather than formatting.

As for editors. There are plenty of editors that support markdown. Many of them even have live previews. So, it's great for that.