The menu is appended to the document with Javascript when the button is clicked, so it won’t easily be converted to work on an HTML-only version of the site.
Here’s where the button is added, you can see it has an action named toggleHamburger:
The toggleHamburger action is defined later in the same file, here:
toggleHamburger changes the hamburgerVisible state, so the menu is ultimately added with panels.push(this.attach("hamburger-menu")); which you can see here: