We are playing against the AI. This game is being played on Emperor level.
Essentially, only the President (or the Designated Player, based on the Chain of Command) actually plays the game. The different departments provide specific input for their areas of responsibility, while the citizenry provides input to the departments, as well as general input.
The actual playing of the game normally takes place in the #demogame chatroom, at specified times. The player tells us everything that happens, and those who are present provide immediate feedback. If anything major happens, the gameplay is stopped and the situation is brought to the forums here for discussion by everyone, not just those who were able to attend the chat. The chat is always logged, and posted here in the forums for everyone to read.
The RPG is separate from, but congruent with, the actual demogame. Actions in the RPG are not allowed to influence the play of the demogame.
There is a whole lot more to it (this forum and 4 subforums worth), but that is the basics, I think.