I'm with you on that intuitive feeling of perceiving the whole screen, but I suspect something is going on for us that is closely related to human sight:
just like the eye is constantly moving to account for the optic nerve blindspot and our brain seamlessly stitches things together, we're probably using our latent understanding of the functions on every part of the screen to stitch together an image/awareness-sense while our eyes actually focus on one part at a time.
When introducing non-computer people to a new application, I find it helps (or is sometimes necessary) to walk them through each part of the screen, explaining what it is for and how it relates to the others. If someone doesn't or can't retain that explanation, usually nothing will help them. But if they do/can retain it, I find even non-computer people are much quicker in noticing particular updates to the application's or OS's GUI.