He starts by looking at the brain's pattern-matching process and the way we learn to model the world around us by identifying common features. (If this sounds familiar, it's because we talked about this in a recent post). He ties this to 'chunking': the way in which repeated routines are linked in our brain (by increased weight to pathways between neurons, if I remember my A.I. lectures of 22 years ago correctly).
Koster states that we get a chemical kick (via endorphins) "at the moment of triuimph when we learn something or master a pattern". It's this that is the primary way of having 'fun', whether it's learning to fit shapes together, working out which aliens to shoot in order to survive, or developing a successful method for getting a frog across a busy road.
Unfortunately the chemicals wear off once we've finished learning, and that's when boredom can set in. (Interestingly, this brings us back to flow (see this post) and the need to balance challenge & skill -- or new learning versus existing routines.)
Koster argues that game-players quickly move past aesthetic & narrative flourishes to recognise abstract patterns in a game, and uses Deathrace & Grand Theft Auto to argue his case that the story & setting are a "side dish" to add some variety to the learning process. (This comes back to the ludology vs. narrative debate.) Bizarrely, he contradicts this stance later in the book when arguing that a game is not just about mechanics but about the whole, illustrating this with the suggestion that a humans-falling-atop-one-another-in-a-gas-chamber game would be morally repugnant, yet would essentially be Tetris in practical terms.
The book looks further into specific contexts of learning, including social & visceral aspects. However, by this stage Koster has lost me as an audience. Maybe, ironically, it's because I don't think I'm learning anything new from him. Mostly, though, I think it's because his analysis is a little too idiosyncratic, adding descriptive flourishes that try to be 'fun' in the wrong way -- a bit like when people want to add 'fun' to Maths to make it appeal to a wider group, yet miss the idea that maths itself can be fun.
This hasn't been a wasted exercise, though. I've learned that the endorphin-producing "aha!" event is important to the enjoyment of a game, and have seen Schell's ideas on modelling & flow reinforced.