In some respects your eyes are correct: if you take the image into an editor and apply a strong gaussian blur to it, you can clearly see the "average" of the strips within each spiral arm are green or blue. This is why the illusion is more effective at a distance: your eyes have surprisingly crappy color resolution, and zooming out has the effect of blurring the colors together.
(And it's also why you completely miss the real illusion -- that each solid color in the picture is really made of tiny red, green, and blue rectangles.)
I believe the more common way to do monitors is to have tiny red, green, and blue dots make up the rectangles. These dots, I am led to believe, are circular.
There are a number of illusions like this - a checkerboard with weird colored tubes comes to mind - but this is easily the most dramatic of the effects. Even when zoomed in, I still see it.
Hmmm, I followed the link in the article to the spinning woman's silhouette - has anyone else tried that one? I don't have enough gif fu to confirm that one, but I have the impression that the illusion is actually that you don't see when the animation changes direction, as opposed to the animation not changing, but your eyes telling you that it did. Can anyone confirm that?
I read an article years ago about people who had a mutation which allowed them higher color picking accuracy. As I recall it had to do with their rods and cones. But I'm not positive.
I wonder if they are able to see that these are the same colors, or if it affects them also.
(And it's also why you completely miss the real illusion -- that each solid color in the picture is really made of tiny red, green, and blue rectangles.)