You can enable it via System Settings -> Keyboard -> 'Keyboard navigation' toggle
Then it works exactly the way the author described (which is also the default on Windows and Linux, I believe)
To be more specific, it only navigates between form elements (including <button>) by default. I was curious why Tab was taking me all over a StackOverflow page but not the one linked here.
Now I am curious why Mac OS has defaults that seemingly break accessibility on some websites? This is the first time in recent memory that I've experienced a page not responding to tab keys at all. Your suggestion remedied the issue on Firefox, but not on Safari for some reason.
[1] https://www.mayank.co/blog/safari-focus#keyboard-navigation
Unfortunately a lot of websites have no searchable text on their links. Sometimes the problem is that it's an icon; other times the problem is that the text is not added in a way that allows search (I don't HTML enough to know all the ways). This is in addition to all the clickable elements that aren't tabbable, ugh.
I've also found a significant number of scrolling/sliding and menu-like elements where tabbing does weird things (partial scroll, not adjacent, etc.).
There was a browser called xxxterm (later called xombrero) that did this pretty nicely. There was a hot key that showed a little overlay of a number on each link. Type that number and it clicks the link.
Sadly the project was discontinued. It was one of my favorite browsers.
If you really care about all websites having roughly the same key binding experience then you need to use an extension or custom browser.
Just to make sure this is not a Firefox issue, I opened the page in Safari, pushed <TAB>, and nothing happened. At this point I'm not sure if the author is performing some elaborate prank on me. I agree that accessibility is important, and being able to quickly navigate with tabs and arrow keys is something that many modern web apps fail at, but some of them do pretty well! (Slack is surprisingly good at placing focus on the most commonly used widgets of the app, and they even provide a mini tutorial on your first attempt at keyboard navigation).
Assuming that this article is not intentionally breaking keyboard navigation, they should hold themselves to the same standards they have outlined.