I am pretty certain you're correct. Those Moire patterns were the ones you see when a fast image-scaling algorithm is taking every nth pixel, not what you should see with different underlying pixel layouts.
In fact, looking at the iPhone zoom, it's blurred in the middle -- it's absolutely had a filter applied to it. You still see some Moire in the center of the image, but that could be a filter artifact.
You'd need the chart rendered at exactly screen resolution, with proper filtering for that resolution (so that it doesn't end up with Moire patterns inherent in the image), and then to display it using code that's guaranteed not to apply a filter. He seems to be using the built-in slideshow apps in all cases (or maybe a browser?), and it looks like the iOS one has a better scaling filter. Which is interesting, but not what he's trying to prove.
On top of all of that -- his photographic resolution can also be coming into play, adding more Moire patterns than you'd see in person. The lower resolution iPhone screen may not have had as much interference with his camera resolution.
In fact, looking at the iPhone zoom, it's blurred in the middle -- it's absolutely had a filter applied to it. You still see some Moire in the center of the image, but that could be a filter artifact.
You'd need the chart rendered at exactly screen resolution, with proper filtering for that resolution (so that it doesn't end up with Moire patterns inherent in the image), and then to display it using code that's guaranteed not to apply a filter. He seems to be using the built-in slideshow apps in all cases (or maybe a browser?), and it looks like the iOS one has a better scaling filter. Which is interesting, but not what he's trying to prove.
On top of all of that -- his photographic resolution can also be coming into play, adding more Moire patterns than you'd see in person. The lower resolution iPhone screen may not have had as much interference with his camera resolution.
So I'd say it's an article fail.