When I do the shape key for the eyelid, it penetrates the eyeball. When I open the source file and slide that finished file's shape key of the eyelid, it also penetrates the eyeball.
Is it something to do with Blender's updates?
From what I see, the same thing is happening in the video too: the eye lid shrinks when closing/opening. It's just that the subdivision surface modifier is turned off, so the lid is thicker and is still seen over the eye ball even when it's shrinking. In the downloadable file, if you turn off the subdivision surface modifier, the lid is almost entirely above the eye ball when moving, but it goes through the eye ball a little. If you move the eye ball slightly inwards, then the lid covers the eye ball completely when it's closing/opening.
I don't know exactly what were the settings for the location of the eyeball when Kent was making this video because here the lid doesn't go under the eyeball, but the eye lid is definitely shrinking. At 6:03 you can see that the edge of the top eye lid is really close to the eye ball... a little bit more and it would have gone under it.
So in conclusion, you would have to model your eye lids carefully, so the interpolation that shrinks the eye lid when going from closed to open doesn't push the eye lid under the eye ball. In this case in particular, when the eye lids are open, only 1/3 of the eye ball is visible. That's why it's possible to keep the eye lid on top of the eye ball during the open/close movement. If you try to open the lids to expose half of the eye ball, the eye lids would have to be way to thick in order to keep them above the eye ball. So it's recommended not trying to open the eye lids that much.
I address and fix this issue in rigging chapter, this lesson lesson specifically I think.