So instead of creating a story you made a mechanic to create a story? Hah. Crafty. You do have at least a scenario or framework all this is happening in, do you?
Of course you actually do not really need it, as something like Minecraft demonstrated. But even that one did implement some sort of hidden goals and a bunch of scenarious on top of the sandbox environment. People like stories.
If pressed for a guess, I might categorize your game under survival, so far.
Anyways, the idea behind having a story would be, to have a framework of mind to ask questions about the game and give answers. Like, does this feature enhance the game. Is this needed. Is that needed. What is missing. What should I put here. What does this need to look like to fit into the narrative. What would these elements do. What elements are missing to compliment the others. And so on.