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What is a game designer? It's one of the toughest questions to answer. Basically, there are two parts to being a game designer.
The first part is communicating, coming up with, and expressing the idea of the game. What the game is, why it is, who it appeals to.
The other part of being a game designer and the different roles in game design are assembling the game from pieces that have been made by the rest of the team.
Game designers generally report to producers or development directors. It depends on the company and what titles they give.
There are various levels of game designers. Ultimately, they will report to a lead designer and the lead designer generally report to a producer or development director.