Show don't tell is a basic rule for a written story, it's very old and accepted by the experts.
But I think we should talk about: game don't show (a new rule I heard about gaming, I think on penny arcade - extra credits, don't remember which episode).
In a game we should express the story using the game challenges.
Ex. in assassin creed you KILL.
Yes, the killing is also showed. But it's not simply a cut scene or a line of dialogue (that are ok for other media such movie or books), the challenge of the game is the main issue to communicate the story.
The story, with some little adjustment I think, is ok.
The question is: how do you plan to implement it in the video game? In which genre does it fit? Why it is good for a video game?
Maybe as a fps. One faction is out to capture you, and the other is trying to protect you, but it's chaos. I imagine something sort of like half life 2. Your working on some research, your walking around in research facility checking all kinds of wild experiments and technology. Then there is a breach of security, and mercenaries start rushing in. You and another secondary character manage to use some tech to escape. This will be a tool which can be used throughout the game which is unique. It could be a cloaking device, maybe something which lets you walk through walls, maybe it slows time down.
I was thinking, it's kind of crazy, but what if it made you keep your mass for the sake of gravity, but allowed you to pass through objects completely unaffected. So, you activate it, and guess what happens? You start to fall into the center of the earth, and you pass all the way through, popping up on the other side of the world. Now your in China, or something. The tools and weapons you use throughout the game have to be very futuristic. You could have a device which when aimed at a persons head, causes them to go crazy, and you could have dial on it to switch modes. One mode makes them fall asleep, one of them makes them hungry or thirsty causing them to stop what they're doing and get some food, another mode makes them very irritable and start fights with the people around them causing a distraction.
Like in hitman, how you have to break into places and be stealthy, and if you get caught, hell breaks loose, you have to break into cool places, to see people, get resources, or obtain items, and you have these type of tools at your disposal, walk through walls etc.