I ask how come shortened URLs are so popular and everywhere? Not the type mentioned in the article.
How and why is the top one better. It's shorter? Neither is easy to remember except one tells you where you are going and what it's all about.
The top URL isn't better. The popularity of the URL shortener came from one simple number: 140. With the advent of twitter, you were limited to 140 characters - including the link you were going to post. if you were to post a link to that Washington Post article on twitter, you'd have very few characters left to actually tell people why you think they should read it. URL shorteners didn't exist before Twitter.
Granted, the Washington Post article URL is horrible. Too many words, stop words (like "a" and "her" which can be removed without any thought/consideration) and plenty of others which probably should be removed. The /wp/ section of the URL seems like it is probably irrelevant too.
A key thing missing from this article, but that iamlost touched on above, is canonicals. When you have two URLs that resolve to the same page (or wildcards like the stackoverflow.com/users/6380/fancy-pants example) you have to make sure you have proper canonicals set up.
Another thing not touched on (though I didn't read all the comments, so someone may have brought it up later) is that it's a UI/UX issue in breaking down a URL.
If you take the washington post example above, each element is a "key" and you should be able to strip off each item and get to a more broad selection that actually resolves to a page. In the Post, we have a department of "Retropolis" and then they organize things by date (rather than category, which is a mistake, IMO, but that's more of a personal preference, not a rule). We'll ignore the "/wp/" portion of the URL, since that should be removed anyway...
If I were to strip the article name off...
This URL should give me a list of EVERY article published in the Retropolis department on the 5th of July, 2017.
This URL should resolve to a page that lists every article published in July of 2017
And this URL should resolve to a page that lists every article from 2017.
This URL should resolve to an index of ALL articles in the Retropolis department.
And, of course, this should be an idex of all news across all departments at the Washington Post.
No matter how you decide to organize your info - by date, by major topic, or whatever - each slash should create a tree of information that you can use to easily work back upwards. People will almost never use it, but it is a HUGE indicator for both user experience and to help search engines understand what a page is going to be about and how it might rank even before the page is crawled and indexed.
Wordpress doesn't do date indexes like this out of the box (though it can be taught to do so). It DOES (if you set up your permalinks properly) work this way if you organize by category or tag, though.