I am only going over four of the most popular genres as they are the ones I feel need the most explanation. The action genre are the bungie jumps of computer games. Action game players are looking for excitement through their game. They want their game playing dexterity challenged and they want to perform grandiose stunts that they couldn't in real life. Because of this desire the shooter was born.
Shooting is obviously a very strong form of action.
To shoot something means that you are capable of destroying it, to be shot, means being capable of being destroyed. Games have succeeded on this since Space Invaders and Galaga and will most likely continue to succeed on it forever. Shooting isn't the only form of action to be found in games though. Shortly after gamers began to shoot their enemies in games, they were able to leap flaming barrels to thwart them instead. Since Donkey Kong there have been thousands of games in the genre of platform jumpers.