Building on what's been said above, the difference in story-telling in Video Games, compared to other formats is the interactivity. Blend the interactivity with the story you want to tell, and you'll have story-telling in a video-game(this, in a very crude way of course). Conventional story-telling in video games, although it's possible, is not exactly something that should be expected. What I mean is, Video Games have the possibility of going beyond what is expected or conventional and when this is well done, it lets Video Games make a name for themselves, as well as it as a medium.
It's been said above that the industry is still very young, and that may be a reason to why the mold hasn't been completely broken yet, along with reasoning within lack of resources, but along with that, I personally think it's because the Game Industry has so much potential, and by knowing this Game Developers can sometimes be reluctant to experiment and end up screwing up - Something which I think is non-existent when trying new things out. The main reasoning behind this I'd say is because the Video Games Industry isn't just an art form anymore, it's a business. And if anyone is going to break the mold, and introduce something completely different, it might just be Indie Developers.
As time passes, as the world and tech evolve, so do Video Games - sorry- so SHOULD Video Games. I love classic and retro video-games, still play them nowadays, but as things evolve we get many more opportunities and resources to bring what we envision to existence.
When we experience a story, we expect to be able to take something from it. We expect to have a sort of epiphany(major or minor) on top of the overall experience. The common keyword among everything to do with story-telling in Video Games however, should be CHOICE. When I have to make moral choices, it brings me a sense of urgency, even knowing it's all just a simulation - But that's just it, a simulation. One of the reasons we like story-telling in Video Games is because even though it's a simulation we still relate to it on so many levels, usually emotionally too.
What is "Story-telling in Video-Game form"?
I think we can't exactly answer that one just yet, precisely because Video Games haven't found the balance between the things it excels at, as an art form, Interactivity - Experimentation(take into account we can pretty much create ANYTHING that we can think of).