Another analogy for game design occurred to me yesterday while making dinner: that of the professional chef.
The human body is capable of recognizing five different kinds of taste (eight kinds of fun). Various foods (games) stimulate different combinations of our taste buds (fun centers in the brain) to produce different experiences in the taster (player). The goal of the chef (game designer) is to combine ingredients (game mechanics) in such a way as to produce a unique and satisfying experience.
Ingredients are not static; sometimes a specific combination leads to a result far greater, or lesser, than the sum of the parts. Some ingredients also give different flavors when raw or cooked. The chef understands how the ingredients can be combined to create certain flavors and aromas (game dynamics) which in turn produce a tasty meal (a fun game).
But the consumer doesn't generally notice the individual ingredients (gourmets excepted), but the overall experience. Because of this, presentation of the meal, with proper garnish and arrangement (cool graphics and sound) is as important as the ingredients themselves. Additionally, meals and games fall into genres based on common characteristics and ingredients... whether it be BBQ / Italian / Chinese, or FPS / RTS / MMO.
Skill of the chef is important; it takes talent and experience to make a decent souffle, and if you get it wrong it's pretty obvious. On the other hand, most people have enough talent to at least follow a recipe (playing a good game in an unfamiliar genre) and get reasonable results. In fact, most people are capable of improvising to create their own modifications to recipes when they want to (creating house rules for board games, either to make them more fun or to add handicapping so that they're more fun for younger players). A few people make gourmet cooking (indie game development) into their hobby even though they never plan to make it their profession. Some people teach cooking classes, but one generally wouldn't trust a teacher who was never a professional chef. And while many of the people taking those classes dream of being Emeril Lagasse, most of them will end up working as a nameless grunt for one of the big-name restaurant chains.
The analogy starts to break down when you compare a master chef to Master Chief...