Perhaps different people experience this image differently. For me, viewing the image on an iPhone, with no squinting at all, the balls look strikingly red, green and blue. It's only after zooming in on the image, that I convinced myself that the balls were brown with colored bars over them. As others have suggested, perhaps a small image size is what makes this illusion work.

Zoom out or move a little further from the screen and try again.

You could even say that actually, the balls aren’t brown. They are made up of pure red, green and blue subpixels on your screen.

It’s really not a particularly interesting illusion.

You're suggesting that this wouldn't work if it were printed or a painting?

No, I’m saying it’s the same type of illusion. Small areas of color blend together and look like a single color to our eyes. (CMYK printing of course works on the same principle)

That's not so clear. The LCD subpixels and CMYK dots may well be below the optical/retina resolution of the eye, in which case it's not really an illusion at all as it's already in the signal data the brain receives. This is quite likely so, because you cannot see those dots individually even with concentration. The same likely goes for squinting your eyes as they become optically unfocused.

In contrast, here the issue is undoubtedly in how the brain interprets the signal data, i.e., an illusion.

Subpixels of modern high resolution screens are below what a normal eye can resolve, but that really isn’t necessary to perceive apparent shades of color. You get the same experience even with a very low resolution RGB screen, where you can distinguish the subpixel elements easily.

It’s not right to say that the balls are “brown”, when they are in fact striped brown and red/green/blue. It’s like saying that a zebra is black if you just ignore the white.

Even then the paint / toner would be a mix of a small number of base pigments in most cases.