I think the author is missing the point. Markdown is easy for humans to read, write, and modify. Yes, parsers can be complicated. Few people need to write parsers, so that's ok, if unfortunate for those parser authors. Orders of magnitude more people need to read, write, and modify the documents themselves, and the fact that it's easy to do so is a huge strength.

HTML is terrible when you consider these properties. It's not easy to read, and is annoying to write and modify. Ditto for any other XML-based markup language, or even something like RST. LaTeX is right out.

Ultimately the author seems to suggest plain text should be what people use? That misses the point. Plain text is great for a lot of things, but if you're going to generate HTML (or something else) from it, you need something that at least has some structure. Markdown hits a nice sweet spot where it has enough structure such that you can reasonably generate rich-text document formats from it, but not so much that non-technical users can't work their heads around the format.