If you try and write in the vidya standard, of the usual boring fetch quests or kill quests, with the usual boring NPC and companion conversations, with an overarching story where the PC is the chosen one, or even if not, you'll fail. It's been done to death and frankly as a writing system it's not particularly good. P:ST is the one time it really worked, but there was a lot of shit there too. It was excellent, but only by vidya standards.
The true potential for vidya story telling lies in world building, random events, lore and set pieces. In Fallout 3, and bare with me now, there were those little set pieces of skeletons with a gun and a box of ammo next to them, or some psycho or jet. It's simple but effective storytelling and worldbuilding, granted, Bethesda sucked at most other aspects of writing and worldbuilding but those set pieces really stayed with me.
Make an open world with compelling factions, make random events feel natural, make the NPC conversations feel natural. Oblivion conversations are a meme for a good reason, but if it were done right it could prove to be an amazing source of storytelling. Just listening to what's happening in NPCs lives, make it compelling. Avoid standard quests, the PC doesn't have to be an active force that drives the story. Make him an observer, and the world itself should be the force that drives the story. Also fuck cutscenes.
Of course, it's obviously easier to program a quest with set paramaters than it is to do something like this. That's frankly the main thing that holds back vidya from actually having believable, live worlds. And that I think is where the strongest potential for storytelling is in vidya.
I'm probably gonna catch a plate of hot shit for saying this, but when I think about it Bethesda really did manage to create some compelling methods of storytelling. The lore and world of Morrowind, random events (even though they ultimately suck in Bethesda games, as a storytelling method I think it's ingenious). Fallout 3 set pieces. Randomized Oblivion conversations, even though it's just a huge meme, and rightly so, could be amazing if pulled off right.
On the other hand New Vegas and Arcanum are obvious examples of worldbuilding done right in the static sense, and that's where Bethesda sucks dick.
And I forgot Metro 2033, that's a good example of NPC conversations done right. Blended in with the atmospheric sounds and guitar music of the metro. There were some awesome moments there.
TL;DR: Living breathing worlds are the best potential vidya has of storytelling, and it's one that books don't have.
Until they perfect it, vidya writing will remain shallow and inedequate compared to actual novels.