The book talks about the benefits of using neural networks in games, the most intriguing of which is the idea that they can learn so as to adapt the game as you play. They discuss four ways that they can be used effectively;
Control
Used for controlling machines in particular to games racing cars. An example the book gives is Colin McRae Rally as the network was trained by observing game developers race around the courses.
Threat Assessment
Training a neural network in game using validation mainly, but in certain games such as strategy simulations they can be attuned to a players particular style of play.
Attack or Flee
You can also use them to control how certain NPCs behave towards others, such as attack or flee. They can learn by positive and negative reinforcement, an example of which they are told to attack and they die they have then learnt not to attack in that situation.
Anticipation
An example of anticipating the next move of your opponent in a fighting game, they discuss the fact that training for this type of gameplay would happen dynamically in game as each game can greatly differ.
The book goes in to greater detail about teaching neural networks but the above ways of using them seem to be the most common.