Whenever I play older games where taking notes helps, I usually write that sort of stuff down on paper. Sure, writing it on the computer would work, but readability is an important factor. Computer text has a sameness to it all that can make it had to tell where something is at a moment's glance. That's not necessarily because it's hard to read, it's just the formatting of the writing itself; it takes much longer to tab something out, do underlining, italics, whatever than it does simply writing it the way you want to begin with.
Also when I think of drawing something I usually use paper as well. I do have a wacom tablet, but it takes a little bit opening up photoshop, and then picking brushes and stuff, and it just slows me down whereas just sketching something is quick because I can just pick up a pencil.
It also helps when planning out how programs will work sometimes.
Basically paper is just good for getting ideas out quickly. Sure, everything that can be done on paper can be done on a computer, it's just slower because you have to open a program and do whatever whereas picking up a pencil and sheet of paper is just so much quicker and easier.