First, a political analysis is about the way people relate to each other. This is why moral and political analyses are often intertwined - politics concerns the rules that regulate the way we live together, and morality is an evaluation of these rules. Politics asks how do we live together? While morality asks: how should we live together? Games are systems of rules that recreate little social worlds, sometimes with the explicit aim of simulating a historical event or the environment of a period in a place. A political analysis of a game is an examination of this little world - what kind of world have we created here? Are we building little towns and trading goods, as in Settlers of Catan? Or are we building a technologically advanced civilization that may nuke its neighbor as in Civilization? Those are two very different social worlds, they give a different feel and they make us treat each other differently.
Thirdly, when you look at power relationships, you develop a special interest in conflicts, and more importantly - in the way the game (or the society) manages them. There are lots of interesting things that rules can do with conflicts - it can channel them to certain places and times (like early or late in the game), it can fan them or try to mitigate them. When players have power over each other, they may use it in different ways. And when they use it in ways that other players consider disagreeable, we have a conflict. The conflict exists, for the most part, in people's minds, it is not just an analysis of who harms who, but who does that as part of an ongoing, unresolved series exchange of blows.
Fourthly, politics look at the roles that the game assigns players. Roles are ways in which we make social rules simpler - we create positions that can be filled by different people and bestow them with powers. Thus, we have special powers that go with specific position, and now we create another interesting political game with regards to those positions. Many games have a special interest in the position of the first player, and there are certain things you get to do as a first player. Moreover, there are certain things you can do to become first player. Other games give more elaborate titles and incorporate positions into the theme of the game - in Dreaming Spires you can be the Chancellor, in Warrior Knights two players get special roles, as chairman of the assembly and head of the church, and of course Game of Thrones has several special roles, including the current holder of the iconic Iron Throne. What does that do to the way people react to each other when one player is sitting on the Iron Throne? I've had games where that person insisted that people address him as 'Your Grace'. And we did.
That's it for now. The first political analysis will come up soon - and it will concern an intensely political game. Later we will analyse politically some games that are not usually considered super political but for now, we're just warming up.