While Justin is absolutely right about the skills needed to be a designer, I'm not sure that's what they're asking for in particular. If you look at it more literally, it seems what they want is documentation that shows concept work (development of concepts, conceptualizing environments, characters, etc), structure (I assume this means structure of the game, perhaps organizational planning of milestones, etc), mechanics (gameplay), and behavior (how different things work in game in relation to one another. For example, writing a flow chart for a choice-based story-driven game).
This is just my take on it. I could be completely wrong. It wouldn't be anywhere near the first time.
The best thing to do if you're unsure is just shoot them off an email and ask for clarification. Ask if they're looking for certain documentation in particular (concept documents, design documents, schedule and budget documents, etc), and what exactly they mean by those terms. Better to ask and have it be an answer you already assumed than to assume and be thrown into the slush pile for irrelevance.