The opening passage of Norman is quite memorable, but I think his best example is the description of the game called "15" which he later reveals to be tic tac toe. Right now I am working on a data understanding project with lots of samples and possibly hundreds of metrics that people could be interested in and I keep hoping that I'll come across a visualization that will make it seem like it's just a simple to understand game of tic tac toe.
That said - the visual representation of tic tac toe as a game elucidates the rules of the game in a way that a child can understand and begin to play. The spatial nature of the game, symetry and the need to perform some blocking moves become apparent quite quickly. What is still missing from this representation is a representation of the "state-space" of the game. A "simple" graph like this would allow one to compute the optimal move in either game as well as allow one to estimate the probability of winning.
I use simple in quotes here because the visual representation require a few hundred nodes if it were a graph. At this level of detail one begins to wonder if the best "visualization" is a look up table.