I think it's a similar vein to speaking about your salary in an open way towards your coworkers. Logically, I don't see much wrong with that behavior but it still makes me feel uneasy. Similarly, I can't really say that I have many reasons against speaking against a company post-firing. If my manager held a large meeting so that my firing was a spectacle, then I would create a blog post detailing my experiences because that would be a very cruel way to let someone go.
I didn't feel like the author was whiny or overly nitpicky but something about the article made me uneasy. It could be because I have the wisdom of the aforementioned phrase "don't burn bridges" in the back of my mind. The author is now less hireable because he made his opinion public. A blog post isn't a Glassdoor comment; a future employer knows that they're hiring a liability that may 'squeal' at a perceived, and possibly valid, slight against him.