I had no idea this was even possible, but the guy in the article has "aphantasia" which keeps him from picturing anything in his mind:

As an artist, I (ironically) find this tough to imagine because I imagine it with an image. This (I suppose trained) reflex makes it difficult to imagine things that are not 3D space-oriented. Like the idea of emergent space-time. I picture it as emerging into a pre-existing volume--which is totally wrong. Or on the opposite end, imagining more than three dimensions I (with great futility) try to picture in only three dimensions.

What the brain can imagine seems to vary wildly from person to person. There was that Batman the Animated Series episode where Bruce realizes he's dreaming because he can't read the newspaper. This struck me as odd, because I can read just fine in my dreams.  Signs or labels often figure prominently.

Also, I dream in color.  Anybody else?

I would think the closest you could come was scanning his brain to see what bits were active while he pictured something.  Of course, you couldn't tell what exactly he was picturing, that his visual cortex was less (or very differently) active than normal.

I do know two people who are "face blind," i.e., they are very poor at recognizing faces unless they are in close proximity.  In one case, being in a crowd makes the phenomenon worse.

I also wonder how much of it is trainable, like drawing. Gross generalization, but the more you know to draw, they better you draw.

I used to work in a grocery store, which inevitably was stuck up one night. The manager who had just spent some unnerving time at gun point decided (in an unfortunate fit of helpfulness) to draw a "composite" picture of the robber for the police.  I exaggerate a little, but it ended up looking something like this:

The police officer brought his partner over to look at it, "Hey, Bob's* drawn us a composite picture."  His partner had to turn away to avoid laughing.

I don't bring this up to make fun of him (he got plenty for weeks at the time) but I have often wondered what the heck was in his head that that came out? I mean, his mom doesn't look like that in his head, right? I suspect it's that he had simply never learned to break down the parts of a face into smaller related parts to get a more accurate rendering.

I wonder if any twins study has ever been done where one twin was trained to draw for many years, and one was not?

*Not really his name.

Then how does he speak? Not just verbalize words, but how does he know what he's talking about? When we start to talk, we apply words to images that we know. Babies start out unable to speak, but able to realize images (or sounds, but I think that's far less pertinent.) We see an image that's moving, very familiar, and has some aspects we recognize. Then we identify those aspects as a nose, eyes, arms, height and build... then we recognize that's Daddy and Mommy. Then we apply a word to it.

But if we didn't have an image for it... how would we know what we were referring to? For example, I wonder how he could talk about a tree if there weren't one in his sight line? When I write "tree", every one of you has some image that comes up in your mind. I'm quite certain that not one of you has a mental sense of "wood, about a foot in circumference, hard bark, leaves, branches", etc. You envision a larch.

This guy doesn't. Oh, maybe he has adapted so that the words DO come to his mind to know that word. But what about a scene? If I tell you that a happy little girl with a red balloon walked down the street with an ice cream cone, on a sunny day, an image comes to your mind. Are those just words with no reference at all?

Yes, there are non-visual concepts, of course, but even then, I suspect that we have a visual image of words like law, hope, photosynthesis, etc.

That's how we learn foreign languages (or at least how I did.) In Spanish, I learned arroz means rice in English - but I knew what I meant when I referred to it because that's what I see in my mind.