Sound in games is as important as in any other form of media. it is used for suspense, drama, action, and atmosphere. Where a film has a scripted soundtrack a game must have a dynamic and intuitive one. this is because a film has pre determined sequences and while this is technically true for games the timing and order can be completely random depending on the player. This requires ambient loops which in theory could go on forever and can be interrupted by the next sequence whenever the player 'chooses'. This brings me to my next point, when a scene needs to change music for dramatic or suspense sequences the music needs to blend to a heightened state, smoothly increasing tempo.
Sound is also used like that of real life where by we use it to locate, be alerted to, or interact with. As in real life you would expect to hear noises created by the surrounding creatures and environments, submersing the player and giving them a fair advantage on the field. In the past sound in computer games was very basic and acted as warnings and ways of letting the player know that an event had occurred. Later games developed sound tracks to immerse the player but still remained very mono-phonic and nothing life like. Back then speech did not exist and was a series of beeps and scrolling text. With the introduction of poly-phonic sound and real sounds games took another step forward and could now talk and interact with the player like never before. In fast paced games objectives could be shouted to the player and they could passively listen while they kept their eyes on the game.
Of course the importance of sound depends on the game. There are so many types of games, unlike the big action and RPG story based games some don't require as much sound. Arcade style games will only use the sound as an enjoyable ambiance or to indicate an event. This is just enough to hold a simple, enjoyable experience.
Overall i feel sound is extremely important in games, as i discovered from playing COD in the labs. The day you forget your headphones is the day your kill/death ratio goes out the window. Putting ambient/dramatic noise aside, just not being able to hear foot steps and gun shots can be the difference between life and death. Game sounds these days are getting better and better with people going out and finding real sounds to record and serious composers getting involved in big blockbuster games. the line between film and games is blurring and sound is a large factor.