On Game Design (again-again)

Thinking about the making of games is something that almost never ceases for me.
Why are graphics important to so many? Where does story fit in Game Design? Why would you place a line between games and play?
It comes down to an understanding of the most basic definition for me. What is game design? Out of that question, subjects arise, such as, is that term even correct, or, how do we discuss art and business in this context.
First of all, the making of a game exists, basically, in a place separated from concepts such as art and money. There is only the crafting. I say that because I have come to understand game design in these three statements:

• Game Design is the arrangement of a persons play in a work.
• The means can be sound, image, narrative, space, culture, language and rules.
• The goal is for that person to achieve a personal experience.

From here, naturally, "game" is an inadequate word, but I still don't think it necessary to use another one. In time, perhaps the meaning of "game" will change.

Business and money are also separate from these statements, but also not excluded. Business simply happens elsewhere, and fits more around the world in which the game is made and released. It's sometimes necessary.

The statements are for me personally to use. If someone agrees, that is good. But I can only argue for the value of the statements, since I have not personally given them a thorough try.