In point of fact this is true of the original photograph. But there the boxes are so small you can't see them. If you have a magnifying lens, try looking at a photograph printed in a newspaper. There you can easily see the array of dots (they use dots not squares) that make up the picture.
When you squint or use some trick to blur the image on the computer screen the picture looks more normal. And if you did not recognize the display as being a picture of Pope John Paul II, you probably will once you blur the image.
In the jargon of imaging science the Pixelized version of the photo removes a lot of the high spatial frequencies in the original photograph and replaces them with high spatial frequency noise. This high spatial frequency noise is removed by when you blur the Pixelized picture and the photo of the Pope looks a little more normal.