The commonly used definition of recycling I've heard is the first one listed on the linked page: "to process (something, such as liquid body waste, glass, or cans) in order to regain material for human use."

That's why the phrase is "reduce, reuse, recycle", right? Yes, technically you could say reuse is a form of recycling, but we distinguish between reusing something outright, and breaking it down into component parts that can be partially recovered -- because we want to point out that the first option is better than the second.