One of the most important attributes of a good designer is the ability to apply critical thinking to any aspect of a game. At a convention recently, a bunch of game developers kept repeating how important critical thinking was. An audience member asked, "Well, what is that really?"
There's this: http://en.wikipedia.org/wiki/Critical_Thinking but that doesn't necessarily give anyone a good idea of how that is applied to game development. One thing we often ask applicants at Obsidian is what their favorite or least favorite games are and why. The "and why" is the most important part of the answer. Anyone can spit out a list of titles to show a wide range of tastes, but that doesn't give us any idea of what he or she found of value in those games. Understanding why -- really why -- you enjoy or dislike games helps you understand what other people may find appealing or distasteful in games.
Lately, I have been trying to take this further. I believe that it is a sign of truly elegant design when you are able to observe a game and determine the goals of the designer of any given system -- and all systems together. Often, you are able to recognize these elements because the game's design leads the player how to figure out when the use of any given tool is appropriate.
I think Pikmin is a good example of a game with elegant design. Practically speaking, the player only has three tools to work with: red, blue, and yellow Pikmin. Reds resist fire and are strong fighters. Blues can swim (and save other Pikmin from drowning). Yellow Pikmin can be thrown higher than other Pikmin and (in the first game) can carry bombs. There are many cases in the game where the player is confronted with a field of hazards and it is up to him or her to determine how to best apply Pikmin to the situation. Often, there is only one "right" way to navigate to the goal, but the player does still have to figure it out. And because the solution can be deduced logically, players typically feel smart -- not dumb -- when they do so. Additionally, the game requires enough moment-to-moment skill in managing Pikmin that player talent is also very rewarding.
Another (very harsh) example of elegant game design can be found in one of my favorite games: Ninja Gaiden for the Xbox. Though not every element of Ninja Gaiden is elegant, many aspects of the combat system are. Ninja Gaiden teaches you through experience that blocking is required in the game. On the first level of the game, the player essentially survives because of blocking. Excepting the boss, no enemy on the level will ever break Ryu out of block. Additionally, enemies attack with relatively low frequency. The player grows to understand that there is a pattern to enemy attacks, typically one, three, or four hits long. When the chain ends, the player can immediately respond (and respond easily, as block hit reactions turn Ryu to face the source of the attack) with his or her own attacks.
This changes when encountering sorcerers on a subsequent level. The sorcerers' fireballs, which are telegraphed by a distinctive sound, will always knock Ryu out of his block if they hit him. The player learns to listen for the sound and instinctively roll at the right time to avoid the attack. Later, the player encounters groups of ninjas that attack with great speed and frequency but (at least in the core game) still do not grapple Ryu. Around the same time, Ryu finds a scroll that teaches the player about counter-attacking out of block hit reactions. The player eventually figures out that counter-attacking is by far the safest way to deal with such enemies. Similar "revelations" occur throughout the game with different weapons, types of attacks, etc.
Think about the games you love and hate and try to figure out why -- then try to figure out what the designers were attempting to accomplish by making the game as they did. It can lead to some amazing discoveries.