HTMX is just a convenient way of handling user-initiated UI updates AJAX calls (for whatever purpose). So instead of writing some JavaScript that looks for a specific element to attach an `onclick` event and subsequently makes an AJAX call then again searches for an element on the page to update with the result you can put some (very simple) HTMX code in the HTML directly and it'll handle that sort of thing automatically; "without having to think."
It's just a nice, convenient way of handling such things. The argument in the article is that "this is how HTML should've been from the start" because it lets you do some pretty sophisticated stuff just by adding some simple/intuitive attributes to the HTML.