ooh, intertesting topic
I thought about it as well, and after much editing apparently I got a pretty organized post.
First of all, I should maybe say that I don't expect the same thing from all games. I can appreciate a wide variety from the most retarded to the most complex.
I guess there are largely three ways in which games appeal:
1. the skill challenge - present you with something to do (shoot bad guys, build cities or arrange building blocks), something that you initially suck at. This makes most people want to prove that they CAN get better at it, and they keep playing and replaying until they kick ass. These games don't need a story or cool graphics at all (look at Tetris!) but they are still the most replayable of the bunch.
2. a good story - I think there are still very few games who truly rely on this. Most of them have a story because it's needed, not because they actually have something to say. Pathologic is a good example, and old King's Quest VI comes to mind as well
I'm sure there are more, but my gaming experince is limited. Now, I actually have mixed feelings about this. On one hand, not having to deal with cliches and infantile excuses for a plot is a great experience. On the other hand, complex stories make the game feel less like a game and more like something else: maybe a book, or a play in which you have to act your part, especially if you want to get 100% of quests like I do. It's a more limited experience than in games that don't rely on a story all that much. (I strongly felt this in Pathologic and it's probably my biggest criticism for the game.)
3. providing an environment to explore - there are games where you don't give much damn either about the story or the skill challenge, but still manage to waste hours casually walking around. For Hicks it's Morrowind, for me - the Gothic series.
Now, I personally think the first category of games, if done right, is by far the most replayable. Build the reflex, keep ramping up the difficulty, and you can hypnotize adults with falling squares of different colors for hours. It just works (probably by stimulating some primitive part of the brain).
The third category is also replayable, but obviously the magic is harder to achieve: "living", large worlds are hard to build, and the matter of taste comes into play as well.
The second category of games are the most interesting, but in my opinion the least replayable. I love Pathologic, it's my favourite game, but I don't know if I'll replay it once I'm done with all three characters. It's like a good book: the effects stay with you longer, it's not a short-term satisfaction, so there isn't much reason to replay it, except perhaps when you're older to see if you understand it differently (as I do with good books).
Edit: Hicks, can you please link to the article you mentioned?