I always used to get tired walking around a city, like on vacation. After a few months of standing, I went on vacation to Paris and immediately noticed a gigantic improvement in my standing and walking stamina. I was the last person to get tired, instead of the first. I could walk around a whole day and be fine!
Beyond that, there were ergonomic benefits for me. I have always found it difficult to use a computer properly in a chair. I'd find myself leaning on a hand rest, or on the desk, etc. These postures are more likely to strain the body. I found myself in minor discomfort and thought: "if I'm going to be doing this job a long time, then I had better find the optimal posture".
The proper posture according to my company's ergonomics advisor is: allow your arms to hang limp at your sides; then without moving your elbows, rotate your forearms to bring them up in front of you, parallel to the ground. Your keyboard should be under your hands in this position. Again without moving your elbow, rotate your primary hand outward (staying parallel with the ground). Your mouse should be comfortably reachable with this movement. If you must extend your elbows, reach, etc., then those motions put you at greater risk for stress injury.
It is very difficult for me to achieve that posture while sitting in a chair - the keyboard and mouse need to be in your lap, basically. (Try the motions I described while sitting and standing and you'll see what I mean.) It was difficult for me to get the right posture while sitting; keyboard trays can do it but are clumsy.
Getting the correct posture in a standing desk is easy: make that "arms out front" motion I described. Imagine yourself standing at a counter with your arms just over it. A keyboard sits under your hands. That's where the standing desk should be, and getting it right primarily entails selecting the correct height of standing desk. The man in the picture/video in the article seems to be demonstrating this pose.
If you work at a computer all day, and likely will for the rest of your life, then you owe it to yourself to get a standing desk. Best office improvement I made in my life. Hope this helps! Happy to discuss further with anyone interested - reach out!