Really long answer, I apologize. Hope it's useful.
I thought about learning from novelists. But it seemed that some of
the skills, i.e. expressing ideas through writing, won't translate
well to expressing ideas through a game.
I thought about learning from screenplay writers. It seems fairly
relevant to storywriting for games.
No, no, wrong idea.
A story is a story, no matter whether it's told through braille, Spanish, or Morse code.
If it has characters, and they do things, it's a story.
I'm guessing you're thinking about this in a manner perhaps similar to this:
Well this book has paragraphs! And drawn-out descriptions, and pages and pages of back-story and details and extraneous information... but a video game is just dialogue, and action! Maybe I can learn from movies, but books, in this case, are surely not my friend.
I am here to correct your errant perspective.
When you play a video game, the only writing you see first-hand is the dialogue, to be sure. But don't ever think for a moment that there aren't paragraphs and paragraphs and paragraphs of description behind the scenes, guiding the artists, level designers, and cinematographers in creating the game and cut-scenes.
Take any story-based game. Take Bioshock, take Halo: Combat Evolved, take any of the Elder Scrolls. All have detailed, fleshed-out worlds with extensive back stories. Every scene in that game has a script behind it. Every character has a dossier. Every ship, setting, and object has a detailed profile, and probably a history. The paragraphs you see in a book are hardly any different from the paragraphs in these miscellaneous pieces of world-creation.
Ever play Halo? Do you remember first crashing on the ringworld, and looking up to see a horizon that rises endlessly into the sky and bends back upon itself, arcing overhead and cutting through the stars like a cartographer's dream?
Anyone who remembers that moment, they all agree: jaws dropped. I've never seen anything like it, and I doubt I will ever be so amazed by a game again.
I assure you that moment had a script, with paragraphs detailing exactly what surrounded the player on all sides: the sounds, the sights, the way the stars gleamed behind the green and blue sky-band, the way the ocean beside you stretched on into clouds. And it was punctuated with a line detailing what Cortana, the player's AI assistant, would be saying in your ear. Something like, Dropships incoming! Better find cover, chief!, if I remember correctly.
My first point: don't ever underestimate just how much written description there is behind something seemingly simple. If it's well-done, there's probably enough paper behind it to fill a small box.
You can learn to write, to describe, to imagine, from any written material, books more than anything else, including games and movies, because they keep your focus on the writing and really allow you to delve into the words without distraction. If you can't happily immerse yourself in words, and learn from them, don't bother trying to write. Waste of time.
The second thing is that you seem to be concentrating on the style and format of the writing, which is why you assume movies will be more useful than books: they're a visual medium.
But as I said, a story is a story. Many stories exist as a book, movie, and video game. Look at Lord of the Rings. You can learn much about crafting characters and plots from books. It's not like a video game plot is so drastically different. It requires the same elements: interesting characters, suspense, constant intrigue, etc etc. Learn how to create these things in one medium and you'll still be able to do it in any other.
But yes, finally, I understand that you wish to learn how to do these things in the style of a video-game. Let me emphasize one last time that you must be able to do these things at all, in the first place, before you should worry about being able to do it in a certain style. But if that's not the issue for you, then yes, movie scripts will translate well. I would advise you to pick some of your favorite movies and feverishly search the web for the official (not fan-transcribed) screenplay/scripts and read them beginning to end, paying close attention to what the author chose to emphasize. Movie scripts can be terse or wordy, but more often terse. They can convey an entire city in a spoonful of words, a world in a sentence. Or they can dote on a little ring for a paragraph. It's all about knowing which elements to emphasize at that point in the story. But this goes for books as well.
You can also find extensive materials behind video games by searching the web. Find the game scripts, the world descriptions, the character profiles and weapon design specs and alien civilization histories and so on ad infinitum. They exist, and they bear more in common with books than you might suspect. They're all important pieces of designing an imagined world.
And yes, there are of course important pieces specific to creating a video game. As mentioned in a comment above, there's a whole field for video-game psychology. But my opinion is that hooking someone with a story and characters is the same in any medium, and as the writer, that's your only job. Leave exhilarating gameplay to the programmers and designers. But remember to make a story that encourages it.
Well, I could have the level script start off with the player having just landed on the beach, about to begin his infiltration of the castle-mansion. That'd be cool.
But...beaches are old hat...what if instead I have him dropped paratrooper-style on the castle roof by the agency, and he has to target his landing so that he lands perfectly on top of the only guard up there, silently taking him out of the picture? And then rappel down the wall? And as he's rappeling down, he witnesses a story-relevant scene through an open window! That'd be even better...