When im looking at the screen and move my eyea across it, my eyes blur.

It does not blur the same way ingame blurs. First this is not motion blur of the subject, its blur because your eyes move. This is different. Don't forget you have a brain too, which blurs things differently than what you just see. For motion blur, it depends how fast it moves and how close is it to the viewer. When you look on a screen, then you look at a single surface without depth information for your eyes and brain. And as explained in the other comments the subject your eyes look at stays still. The subject does not have any motion.

The blur you get from little movement looking at a screen that does not move is completely different from ingame motion blur that selectively activates motion blur on the scenery.