It's not enough with being an expert player — you must have something to say about it. You may be an expert player of X game series, but describing your prowess in the game, or regurgitating press releases of the game will not make for a good assignment. Both assignments complement each other, and the goal is to help your reader (which can be anyone, not only the instructor) learn something novel about the game, saying something about the game which may not have been said before.
Choose a game that will allow you to provide that kind of insight, either because you know the game well, or because you know it may have interesting aspects to discuss. Some approaches which may develop into successful papers are:
- discovering an obscure or cult game and explaining how it subverted the expectations of players.
- discussing the values in a videogame, and their implied morality as incorporated in the game system, contrasting the values of the story of the game to those of the mechanics.
- exploring how a game constructs its space within and beyond the screen, and what may constitute the "magic circle" (or not).
- providing an alternate interpretation of a game, inspired by the readings of the class.
- discussing how a game may straddle between being an interactive story or a game.
There are many, many approaches to analyzing a game—if you're not sure whether yours would count, check with the instructor.
You can choose more than one game, if you're aiming at writing a comparative approach. If this is what you want to do, please check with the instructor first, to make sure that a) the comparison is relevant to the class and b) to make sure the discussion will address the connection in enough depth. If the analysis is comparative, your first paper should consist of what the initial points in common / of contrast are, and why is interesting; the second should provide the reader with how the comparison teaches us something about both games.
You can choose more than one game, if you're aiming at writing a comparative approach. If the analysis is comparative, your first paper should consist of what the points in common / of contrast are, and why is interesting; the second should provide the reader with something new about the game. For example, in comparing System Shock with Bioshock, the first paper would trace the historical relationship between both games by establishing the points in common of both games (development teams, first person view, sound recordings) and differences (fictional worlds, use of non-player characters). The second paper can focus on how each game shapes the agency of the player, and how it relates to the fictional world of the game, based on the commonalities and differences established in the previous assignment.
It is okay to have played the game already, but remember you'll have to replay it for the assignment. Watching replay videos as a refresher does not fly—it is obvious when you have not played the game recently. Yeah, really.
The first paper is a first approach to the game. In the second paper you have to prove your expertise by having played it extensively—maybe your insight is different from what you first expected, but it's okay.