For the most part, there are very few games I have continued playing to 'find out what happens'. With most games, once I am no longer feeling invested in a game's mechanics (or I've just 'got it' and it's feeling repetitive) I stop playing and move on to another game. For an actual plot to grab me and give me the motivation to finish a game... it's rare stuff. It's also my metric for a 'good story' in a game.
Last of us, Heavy Rain, Catherine, Breakdown, Shadow of the Colossus, Kings Quest 3... these are rare examples of games "worth playing to see what happens", and they used massively different techniques and styles to achieve that result.
Looking at reviews though, those games get praised for the stereotypically broad definition of 'writing'. Even major reviews don't have a common grip on what "writing" is. Regardless, it's refreshing to be at GDC and see discussions about specific aspects of narrative, setting, background, etc.
Personally though, I have three strong opinions on the topic of "story" as it pertains to games.
1) Despite the excellent examples of plot driven games I listed above, what I truly value in game writing is simply dialogue. At the end of the day I really just need the actual words coming out of a character's mouth to be even vaguely relatable. I barely even care if it's 'interesting' as long as it sounds like something you might actually hear from a random person in the real world. If you've got relatable dialogue you've got a lot of credit towards the general perception of a game with "great writing" IMO. You don't get paid per syllable, and it's not an intelligence contest; just talk like people talk and don't over think it. To a good degree the desire for relatable characters plays into my second strong story opinion...
2) I really don't give a shit about 'saving the world' in a game. I'm sure you can read into that cynicism about solving modern political issues, but really, who relates to that as a goal? Stop it. We as humans have so many common experiences already, it's a waste not to use those shared experiences and craft a story around relationships and events we actually deal with in our lives. Do I care about stopping the international terror organization from breaking the super virus vial, or do I care about saving a loved one? My list earlier of 'games I play to see what happens' involves very little 'saving the world'. With rare exception you already know what happens when a world needs saving, *gasp* the world gets saved! (Yeah yeah, hush, astute reader! No spoilers in comments!)
3) Don't Techno-MacGuffin me. Regardless of the overall plot arc, I *completely* zone out the moment someone starts squawking at me to "isolate the permashield reactor before the rezosphere updates!". Again, just keep it simple and don't overthink it. Use concepts that can translate to actual words. Anyway, nine times out of ten I only need to shut down the 'Pleseopod Device' because it'll let me save the world. (We already know I'm apparently fine with a total global reset ;-)
I hate to paint with such a broad brush, but these three issues are part of why I have such a hard time completing many FPS campaigns, and many (*not ALL*) JRPGs? Hell, I had what I can only describe as 'violent bodily rejection' to watching the FF7 Advent Children movie.
I also know I am beating the "relatable" drum pretty hard.
The moment where you sneak off to the bathroom to check your cell phone in Catherine, the moment the wizard Manannan leaves you alone in the house to work your mischief around your chores in Kings Quest 3, the time you're fearing for your safety as a woman in her apartment with intruders in Heavy Rain... those moments are lifelong gaming hall of fame magical moments. I think back on them years later and grin out loud.
I dabble with writing based on necessity for making games with only a couple people (and zero outsourcing). After Epic I wrote most of our adventure game Lili. There's a crime of a "techno MacGuffin" at one point, but it was due to an unforeseen production change. There's also a big bad guy to defeat, but that's more of a hook for gameplay reasons. It also needed more editing, but overall I was very proud of the results (and Lili's writing had some acclaim from people whose professional opinion I really value).
Aside from trying to be funny and writing with the same casual nature as one would use on FaceBook with friends, we tried really hard to give Lili a story we could all relate to. We went with Lili having conflicts about her career after school. There's pressure from Lili's father to follow in his path, she's interested in doing something for herself, and it's chock full of paraphrased conversations I've had with real people like my wife.
Bottom line, I don't consider myself a "writer" any more than any other developer who takes it on themselves to write their own games... but I found that the three things I felt strongly about when playing games was also a great guide for the first time I had to write something.
Thanks for reading!