Subtractive design is an expected-but-unintentional occurrence if the project is running over scope. And the stuff that is subtracted is dependent on the size and status of the project. Big budget games will typically cut large swathes of content and some of the less-critical features. Small budget games may end up gutting the entire concept in favor of whatever gets some gameplay with the available assets and tech.
It is a meme, almost a cliche, for designers to battle programmers over the quantity of features in the game, because more features (usually) allow more gameplay. There's a lot of inertia to avoid cuts if possible; a cut is viewed as "wasted effort," and each one potentially violates the interests of stakeholders.
On the other hand, if you view games as being like other art forms, it's not uncommon for other mediums to overproduce and then cut to reach the final product: Pop songs are cut to about 3 minutes, and movies get cut to about 90 minutes. Big budget games have been steered towards shorter length recently, but this is done mostly because it costs too much to produce 40+ hour games at the current quality bar, not because of a move towards "cut to perfection" methodology.
It's more than that. A designer's fundamental job is to distill the essence of a presentation to it's more powerful form. That means not only taking a clunky version and paring it down; it means reimagining what the piece fundamentally is or does, and presenting it in a way that conveys the actual meaning--not just what you thought the meaning was.
With games, it means figuring what makes it fundamentally engaging, then presenting that in a way that capitalizes on those aspects that improve it while cutting those that add nothing.
Designers/film-makers use it a lot to draw attention to particular subject, such as the all B&W except the girl in red coat depicted in Schindler's list was perfect example.
It is a meme, almost a cliche, for designers to battle programmers over the quantity of features in the game, because more features (usually) allow more gameplay. There's a lot of inertia to avoid cuts if possible; a cut is viewed as "wasted effort," and each one potentially violates the interests of stakeholders.
On the other hand, if you view games as being like other art forms, it's not uncommon for other mediums to overproduce and then cut to reach the final product: Pop songs are cut to about 3 minutes, and movies get cut to about 90 minutes. Big budget games have been steered towards shorter length recently, but this is done mostly because it costs too much to produce 40+ hour games at the current quality bar, not because of a move towards "cut to perfection" methodology.