That chooses to tell its story largely through writing.
It's only fractionally through writing if we define writing as text - I'm not really clear on what you're using "writing" to refer to here. Again, think about The Glow. In a novel, the author would describe the location, and how the Vault Dweller feels upon entering it. In a movie, set designers would work to portray the location, the soundtrack would enhance the mood, and an actor or actress would portray how the Vault Dweller feels.
In a videogame, graphics artists portray the location, the soundtrack enhances the mood, and then the player controls the protagonist, their own emotional responses being that of the protagonist (this isn't even unique to RPGs; Gordon Freeman and (early) Lara Croft are examples of silent or mostly-silent protagonists whose reactions to things are intentionally blank so that the player's own thoughts and feelings may be projected onto them - it's one of the primary ways in which videogames can achieve a different effect to other mediums).
The point is that all these mediums are attempting to do the same thing, which is to bring about an emotional response in the viewer/reader/player. They use different tools to do this, but none is inherently better than the other (at least not overall; some may be better at certain things). If you think Fallout as a game is not as successful at this as a novelisation of the same concept would be, that's a fair opinion but I don't see how it translates to "videogames don't need writing". I think it's folly to compare mediums like this anyway - videogames can have bad writing and very frequently do, but to act as if the audiovisual component of a chiefly audiovisual medium is unimportant is bizarre, as is pretending that videogames don't offer unique ways of storytelling that don't exist for other mediums, and that these can't be successfully used by good developers.
Case in point, Mount & Blade is not a game "without any writing". Calradia is visually designed to evoke a certain time and place, the dialogue of the characters frequently illustrates the feudal/class system going on and the cheapness with which human life is viewed in that world, the music (peaceful music while traveling, intense music for battles, heroic music for moments of triumph) is meant to elevate the mood, etc. Calradia has a very strong sense of place, and inspires certain moods and emotional reactions in the player. If by "writing" you literally mean "text on the screen" then sure, but given that you conflated it with "storyfaggotry" I'm assuming you're using it to refer to basically any stylistic element that exists separate from mechanical gameplay; Mount & Blade is a game rich in these elements.
Given that you drew a distinction between "environmental storytelling" and "writing" - which, to me, are synonymous - I think there's some kind of semantics issue going on where nobody can quite tell what you're trying to say or what you mean by "writing".
