There's nothing to refute in your post; you only told the audience that you don't get OP, and people tried to explain the appeal to you. What you do with that information is your thing.
None of what you said explained the appeal of OP's technique! Using JavaScript doesn't have to affect your reliability, accessibility, SEO, or any of the things you said. How am I supposed to do anything with useless information?
If anything, hiding the hamburger menu behind an HTTP response is *less accessible*!
Not to mention the article's menu "close" button relies on JS to send you back to the correct page, and doesn't work with open in new tab / window even with JS enabled.
If anything, hiding the hamburger menu behind an HTTP response is *less accessible*!