Here is my theory. Game criticism isn't about telling the player whether a game is fun or not. If that's the critic's job we are all in a lot of trouble, because in the near future everyone will be able to pick up a demo and tell themselves whether a game is fun or not. “Is it fun?” is a question destined for obsolescence. We should be telling people how a game is fun.
I think this task is a something like what Aristotle does in the Poetics. Aristotle thinks that there is a certain experience that is constitutive of tragedy as an artform: katharsis, or the cleansing release of pent-up emotion and pity. With this end in view, Aristotle asks how the various elements of the dramatic work (the plot, the characters, and so on) need to be structured in order to create this emotion for the audience. And it's the same for games; what a critic can do is explain how the various elements of the game-- the visual design, the narrative, the gameplay-- conspire to create pleasure.
The second question, then, is what kind of pleasure do games aim at? What is the gaming equivalent of katharsis? My answer is that games aim to inspire a characteristic sort of pleasure, the delight in the discovery and mastery of rules. Play is an expression of the human mind's native lust to master the lawlike natural world through experiment and planning. As Kant says: “The understanding is hungry after rules, and it is satisfied when it finds them.” And video games are most fitting artform to satisfy this desire, because unlike other games and sports the rules of a video game are not disclosed in advance. Each game reveals a novel rulebound world to the player, and asks her to uncover its underlying logic through inquiry and imagination. And that is why the games are fun to play.