It's not so much becoming an artist as training your brain to make a thing on paper based on what you see or what you are imagining. Heck, draw the same thing every day – someone's ear is a good one – and watch when you get better and better.
It's very much like photography and cinematography and ties into what the author is trying to achieve by telling someone to draw.
You see differently when you have an objective. Just as you train yourself to see opportunities when becoming an entrepreneur (and realize ideas are 'worthless' because there are too many of them to chase them all down), you will train yourself to see that the world is not just lines, but degrees of shadow and reflection.
I was a professional artist (painting, sculpture, drawing) before my software career and when I've been out of practice for a while, I find that I lose this faculty. A little time over the table with pencils, some clay, or watercolors and my brain clicks back into seeing and not just glancing over things.
I agree that just drawing, design theory, writing, and ux are not guaranteed to make you a brilliant, original, designer. However, understanding typography, whitespace, color, and being able to apply that to a goal is a big lever.
I always encourage "back end" developers to work on design. Even if it's bog-standard bootstrap with some tweaks, it ends up being better for a client or an employer. Keep in mind that most web apps lack pulchritude.
Plus, I hate it when people refuse to do front-end work because they're "back-end" people.