It's not very exciting since it just paints the screen white, it all comes down to WHEN the sensors SEES the exact blob of white it's focused on thru that plastic lens during the draw you see slowed down in the video posted (it's dumb, it just picks up on the light which is basically a 1930s technology), then it can do the math and figure out where exactly you're aiming (or not aiming, if doing a point-away RELOAD such as Lethal Enforcers) and apply any offset formulated during the aiming calibration done when setting up the game (i.e. +10 pixels on X-axis). Nintendo does it differently and much less accurately. It strobes quickly with 'targets' of black blobs flashed in sequence and only knows if you're connecting with a target region, it never really knows exactly where you're pointing and doesn't care, only if you're a match for target 1, target 2, etc. It would be more exciting to see in slo-mo than the other method, though.
I know I answered an unasked question but I enjoy the subject matter.
We also see the TV's picture due to our human brain simplifying things through something called "persistence of vision" which allows this rolling blur of light to make sense to us, but animals supposedly see something much different.