Markdown does have a spec created and posted by the person that invented it, John Gruber[1]. The problem is that people keep adding features to it and no one follows the actual markdown spec.
That's not a spec, and it doesn't claim to be one. It's the syntax description that I referred to above. A spec needs to unambiguously <em>spec</em>ify the grammar.
John didn't invent it for everyone to implement it on everything on the internet. He invented it for him to use on his blog because he's a writer and wanted to focus on his content, not on writing HTML. Just because it's not "specified" that doesn't mean it's not the canonical spec. All of the other additions that aren't on that page aren't based on the canonical version of Markdown.
[1] - https://daringfireball.net/projects/markdown/