I've seen this called a "basted egg"; the term originally referred to spooning hot fat from the pan over the egg while frying, but now also refers to simply frying an egg in a covered pan, allowing steam and hot air to build up and cook the top. I'll refer specifically to the second meaning, as it seems to match the video. Incidentally, I have never heard anyone call this an "over easy" egg.
Of course, if you wait loooooooong enough, the top of the egg will cook, and then dry out, and eventually catch fire. But if you find the yolk is cooking hard on the bottom before it's cooked to your liking on top, things to do:
- Use a smaller pan so that a thicker steam builds up
- Preheat the lid. The easiest way to do this is just to have the lid on while you preheat the pan.
- Add a spoon of water to the pan just before you cover it. You can do this right after adding the egg, or at any time if you think the top's cooking too slowly. The steam here is a little bit localized, so if you notice one side of the egg (like, left or right, not top or bottom) cooking more slowly, this is an effective way of correcting that.
You can combine these tips, BTW. I add a spoon of water to the pan when I start preheating it; by the time the pan is up to temperature the lid has been steam-heated and the water has boiled away.