So, a choise based story game...
The first thing that came to my mind was 80 days from inklestudios, which is - as one can guess from the name - something that's based on the famous book from Jules Verne.
It got a pretty art work which is... coherent (hope that's the correct word), a fitting but non interrupting music and sound environment and... well, here is not the place for a review, but you can grab it from steam or as app (steam version should be more rich in terms of features).
There are many other games around on steam, like that one with the boat and underground London where you die (way too much for my taste), so go ahead and get first-hand experiences about how others did make narrative games.
But don't make the mistake and assume that a good story is all a game needs. Well... way too many games do have a lame story but still sell, because as a type of media games can compensate for bad story by fine looks or other stuff. World of tanks offers no story after all (except for the wrong history) but draws in too many gamers. At the other side, adventures these days lack a huge audience, because the new generation of consumers cannot think and is overwhelmed with controls that require more than one button to press *sigh*.
But how to draw in a gamer using nothing but a story? I still keep on wondering if it would be a better idea to just offer a huge load of example games and tell how they are good in terms of story, but... I think this isn't the right way of doing it. At least not here.
So explain how to produce a well-written piece of a story may not be my strong point at this moment (yet...); there are others which are better in that. But I know my way around game design and will try to offer some advice.
Living world - whatever the story is about, if the world it unfolds in does not respond in a way noticeable, it will lose much of its charm. Like in many RPGs where you can rob the entire town of their valuables without anyone caring. It will be hard to keep track of what caused what, but it needs to be clear why stuff happens in the way it does when this was caused by something the player did earlier. That's something pen and paper masters usually are pretty good at, but nothing you need to take care about inside a book... no, wrong, you don't need to keep track all the possible outcomes, just one, which is way more easy.
colourful NPCs - the not protagonists in stories usually fall a bit flat, because not everyone needs a deep backstory to appear for a brief moment inside a book. But in a game, chances are good the player will encounter some uninteresting background-NPCs over and over again... if they do not have a purpose to fulfill, but can be interacted with, you will confuse the living daylight out of your players. By the way, the living world applies to them too, even if it's just them talking about what the player did like they heard it from someone else. Even more, you can use company-cubes... eh NPCs to push the player in the correct direction by dropping hints about what will happen if things are done this way or that way.
keep your artwork in line - huh, nothing about the story (again)? Yes, because the background is where much of the story will unfold. You do not need lines of text to describe something you can just paint. Such graphical pieces of story will be able to transport messages and everything you would need to describe using way too many words by just being there. They can add Color to your NPCs and Life to you World. When you crash a huge UFO and it does not appear in the scenes a player would expect it, it will be rather strange. At the other side, you can tell the story by adding military around it and never waste a single moment of game flow by having the player need to read about this happen.
the Skyrim/Oblivion Variant of Storytelling You can use most of Bethesda's games for this, but they just put a burned down house right in the middle of nowhere and a smoked note about "add this and this and DONT ADD THIS". Finish. No text, no telling needed; a curious player will go try out for himself what happens if you combine these things. And if he blow up himself... well, what did he expect to happen?
Don't punish! Most important for every game I think - if your player didn't do something the way you want, do not punish him hours of game later. If you need an artifact to continue six levels laters, but that artifact was hidden somewhere in the first level, and the game cannot continue because of that... that's bad game design. And it will be the dead of every game.
Okay... I need to keep it short this time, so these should be sufficient. Last but not least: What the others did say is pretty important for the general storyline.
- have a character with a believable motivation
- switch between high tension and relaxation like in a good act
- have the world being believable
- and never leave the house without your towel
- oh and don't insert forced (stupid) events... yes, I look at you Mass Effect
Never mind the last one. But one last piece of advice still remains:
Reward your player - while the story can be lame, you need to reward your player for processing in the game. That is how to keep him motivated. Collectables where used for this, more skills and so on. The player must feel that he moves in the right direction and notice that good process is being made. Sadly, a good story is just secondary to this.
Aaaaand... I'm afraid that isn't even Writing.StackExchange territory any more. Still, I have to repeat: game design and keeping the gamer encouraged isn't done using a story alone. Its a collage of all the media game offers.