When I think about good stories, especially in videogames, there's a handful of bullet points that shapes that idea for me in broad, yet recognizable strokes. Not being a storyteller kinda takes some weight off my opinions, but I'm gonna try to sort them into a reasonably coherent whole for the sake of discussion.
In videogames, stories first comes to life as basic ideas about the main characters, their goals and the settings, and the plot gradually unfolds through many iterations to make sure that the technology at hand supports the events. The process involves lots of flexibility from both the creative and technical parts of a team, often working under strict time constraints. So when we come across a well arranged and presented story, it's usually the result of an efficient dialogue between various aspects of development, and the developer's ability to conceal the underlying tradeoffs of said efficiency.
The best stories are arguably those
that provides peripheral events
that are just as carefully
thought out as the main ones,
and thematically/emotionally
tied with the latter
The complexity of the process kinda slants the art of game writing towards being on point with its contents, and making the most out of what you can work with. A good writer can take a single location and flesh it out deeply, inserting elements that hints at its own history and at the same time, resonates factually or emotionally with the events in the game and/or the feelings of the characters.
Interactions and audiovisual cues goes a long way towards establishing moods, creating anticipation and telling us something about places and persons. So even in relatively limited spaces it is possible to establish what some calls "sense of place", a communicative microcosmos where a player can explore and figure out things that goes beyond his current time and/or space.
As a modern medium, videogames incorporates a rich language derived from photography, literature, movies, music, architecture and more. It's a highly versatile language that demands research, awareness of the scope and goals for which it's going to be used, and the sensibility to make everything - characters, environments, events, motivations, cause and effect relationships etc. - come together meaningfully. However, more often than not, it ends up being utilised far below its potential: what I feel are the best stories manages to create connections - some immediately apparent and some left to player discovery - between the language's elements, mutually elevating themselves towards a sense of richness and depth that is the very spearhead of game writing.
As in any other form of art including an element of composition, good game writing becomes a matter of economy, so it's not entirely wrong to assume the existence of an unwritten rule about the ever looming risk of overexposure: never show what you can hint at, unless it's absolutely needed. With the sensorial arsenal at its disposal, the language of videogames is just
terrific at hints, loosening the dependence from words and inviting the authors to choose them carefully. So the game writer mainly provides what we might call a direct view on things and events, but at the same time he can enrich it through other elements of the language to form a peripheral view - something the player feels and can be compelled to explore.
I feel that narrative rewards in videogames can be just as powerful as material (=gameplay related) rewards: they can help you flash out mysteries, relationships and personalities; they can provide foretelling or explanation for future developments in the story. Building a web of indirect references is an important skill for game writers as it greatly contributes to plot coherence, helping the player feeling invested with the story and the characters. The best stories are arguably those that provides peripheral events that are just as carefully thought out as the main ones, and thematically/emotionally tied with the latter.