The temporality of computer games is a significant aspect for understanding the metamorphosis of social time in the digital age. We can say there is a transition from planning on the basis of universal social time to coordination with the help of opening time pushing its boundaries. Focusing on computer games in family everyday life we can understand both the features of the game temporality and family time. The topic of computer game time was developed in our empirical study of the early game socialization of children. 29 semi-structured interviews were conducted with parents who have children under the age of ten. We asked about the children's game experience: from what age the child plays computer games, how the parents control this process, which is usually discussed on the topic of game in family, etc. Computer text-processing of the interviews identified the leading of time vocabulary in parent's narratives. A time appears as a tool for direction and guidance to children. We discuss that computer games take not only time what was spent previously on other activities, games have its own internal time in which a gamer enters and begins to act.