From about 15 seconds into the video (link below) Notch starts apparently coding while the game is running - and having it magically reflect his changes. I tried to stop/start the video in a sort of frame by frame manner. I notice just before he starts doing it, a properties window of some sort pops up but I'm too slow to catch it. I can see that he's using Eclipse and I understand that he uses LWJGL for his games, right? The make-up of the game seems to be an applet (I have limited experience with applets).

Does anyone know how he does that? Is the application actually updating to reflect code changes without having to go through the close/build/run sequence?

http://www.youtube.com/watch?v=KcfFJ6pNEZk

You can do that when you are running in debug mode (see that little button next to the run button, the one with the "bug" icon?). Eclipse hot-swaps the new bytecode in while your app is running.

if you get used to it's very comfortable
change everything while the game is running and stuff

Any IDE should be able to do hotswap -- it's a java feature, not an IDE feature.  The built in hotswap is nice, but for real pro work, JRebel is where its at.  Notch I'm sure can afford a JRebel license.