Interactivity is the obvious demarcator when defining videogames in contrast to older entertainment media. Linearity is supposedly a corollary of this: VGs, being interactive, are nonlinear, while films/TV shows/books are not interactive, and are thus linear experiences.
But is this idea consistent with actual patterns of modern consumption? Specifically, does playing a videogame allow for the player to consume the content outside of the designer's intended structure? Is a reader or viewer capable of consuming a book or movie/show with disregard for the creators' intent? While abhorring an Absolute, I'd say No & Yes.
I know people who skip to the end of a book to see the ending (in both fiction and non-fiction). Before purchasing the item, they want to know if it's "worth it". Whatever happened to "it's the journey not the destination", eh people? Further, DVDs allow the viewer to skip around to any point in a movie/show they wish; streaming media allows instant replay of a moment or scene, and given buffering, jumping ahead as well. However, you can't simply skip to the final boss, can you?
The content of older media is static, and thus encourages nonlinear consumption (at least in repetitious consumption), but the content of VGs is dynamic (to varying degrees, of course) even as the consumption of that content is linear (for the most part).
Granted, there are exceptions to every rule, but I think that the concept of linearity in games is popularly misunderstood. The linearity of an experience, when measured against the creator/designer's intent, seems to be most stable within the medium of videogames: the audience must follow the cues of the code, not the whims of their thumb.
There are lots of ways to disagree with me, and I'm happy to read them =)