Actionable advice: Set up a program such that you have an array of pixels. Say, 512x512. Now write a while loop which randomizes those pixels. Finally, figure out some way to "create a window and put those pixels on the screen."
You now have a game loop. This is roughly how every game works at a basic level.
The next step is to realize that a triangle is the fundamental way to draw shapes quickly. Want to draw a square? That's two triangles. Want to draw a humanoid? Sounds complicated, but artists approximate humanoids with a combination of spheres, cylinders, cubes, etc. And all of those can be divided up into triangles.
So a triangle is therefore the first place to start in understanding graphics in general. What's the goal? "Create a data structure to represent a triangle. Now try to draw a white triangle into your little pixel array."
It's going to be tough. But tough work is good. I remember how difficult it was for me to even get a basic white triangle up on the screen. But the rewards are worthwhile, because at this point a lot of other things will start to click. A "vertex buffer" will no longer be mysterious, for example, because you'll immediately see that your triangle structure (whatever you came up with) was really just "a vertex buffer with three vertices." And then you'll start to wonder why graphics programmers came up with such complicated words to describe such simple concepts...
At this point, you'll have the ability to go in one of two directions: "Notch" or "Carmack." It depends entirely on what you find interesting. If you like the idea of making games, concentrate on creating Pong. (You have everything you need, because you just got a triangle up on the screen, after all.) If you like more along the lines of what the article talks about, then concentrate on creating a software rasterizer. "Software rasterizer" is another one of those terms that turn out to sound scary, but is way easier than you'd expect. It's hard in the same way that learning to ride a bike is hard: it'll take awhile, but you'll never forget it. After that, nothing else you ever do (in graphics) will ever seem even slightly mysterious. I have some thoughts on how to learn the latter, if anyone's interested.