For instance, I might write a journal entry in which the villain reminisces about a love song he wrote for his wife. Then, I may suggest to one of the designers that he place a roughly carved wooden pipe into an environment which we know the villain has visited frequently. My story won't answer these questions directly but if I do my job right, it won't matter. The player's own answers fill in the missing pieces, making it a richer story experience overall. It's a much more collaborative writing effort.
People become involved in a story the minute they try to interpret what's happening.
Given a few scattered pieces of information, they'll try to figure out what each piece means, and how it fits into the overall plot. Half the fun of any story comes from forming theories about the ending and then seeing if your suspicions will be proved right. This is as true of the story in a nonlinear puzzle game as it is in a linear novel or film. If they aren't, the story won't be any good. And yet, I can't predict which pieces of story the player will encounter first.