Story and Game Structures can be Artfully Merged with Indirect Control
"Freedom" is a distinct difference between story and game play - the story is on rails, and the audience is along for the ride, whereas a game puts the player in control of the action.
But in truth, that freedom is an illusion: a game is a controlled environment with pre-defined parameters, and the player's "freedom" to act is limited to the choices provided to them within the context of the game.
So one of the tricks of game design is giving the player the sense of freedom, to draw his focus to the elements of the game over which he is given control and away from those over which he does not.
Options
The author begins with a comparison of a fill-in-the-blank question with a multiple choice one. The empty space provides the user with more freedom, but most students prefer the multiple-choice option, as it gives them better chances of success (less opportunity for failure). Instructors also prefer multiple-choice, because it's easier to grade.
The same is found in retail: customers feel overwhelmed in an ice-cream shop that has a hundred flavors, but are able to make a selection quickly in a shop that offers only five (and in the end, enjoy their choice just as much, and feel they had just as much freedom of decision).
One compromise the author suggests is to provide a menu of the most popular options, but to have others in reserve in case someone had a specific desire for a flavor that's not on the menu. But at this point, I think he's stretching his own metaphor.
Goals
In most games, the user does not choose their goal: they are told what their goal is, or in some instances, are given a handful of possible outcomes to choose among (Civilization can be won by diplomacy, conquest, cultural superiority, etc.).
As with constrained options, players prefer constrained goals. A game without a goal, where you wander around aimlessly and play in the environment, is by definition a toy and not a game.
Interface
The interface itself is a kind of constraint: there are only so many things a user can "do" with a game controller, mouse, and keyboard. Even in games that provide their own interface hardware (a gun for shooting games, a steering heel for driving games, a "guitar" for a music game), each controller has a finite number of ways the user can interact with it (that the computer will recognize).
The same is true of the avatar in the game: its motions or capabilities are constrained to what the designer provides to them. A Sherman tank cannot fly, or even jump very far, and the player accepts these constraints.
Design
The design of the game environment (the "board" imposes constraints. There are hard-and-fast boundaries to the playing field that the player may not move beyond.
There are also design techniques that do not impose a technical constraint, but which focus the user's attention on a specific element of the screen with which the user is supposed to interact. And while it is "highlighted" rather than controlled, the user generally goes for it.
Character
The characters within the game are a constraint. Every character in the game has been placed by the designer (the player cannot choose a character the designer has not provided as an option), and the behavior of characters is controlled by the game.
Additionally, the action of the characters (their ability to harm or reward the player) motivate the player to act in certain ways - specifically, in ways in which the designer intends for the player to act.
Music
Music is important in games: it provides audio cues that can provoke a Pavlovian response. The user quickly learns the sound effect that has a certain significance (a prize is nearby, there's a hidden area, an enemy is approaching, etc.)