Sports, action games, console shooters, racing games and more are all played in real time. However, like weight and mass, game time and real time are not the same thing. They only appear to be so under certain circumstances.
Game time is measured in ticks. In real time games, ticks are identical to framerate (frames per second) and so blend together to seem continuous, but in games like Chess a single tick is as long as the gap between turns. Game time can also have breaks, pauses, starts and ends, such as when you save your progress in a roleplaying game to come back tomorrow and play some more.
Some games use game time for interesting actions and rules, such as the time travel element of Braid or the bullet-time mode of Max Payne.