It is mainly children and adolescents who are involved in video gaming. The lockdown caused by the COVID-19 pandemic may have further increased their use of video games and, consequently, the risk of gaming disorder (GD) symptoms. However, currently, we do not have exhaustive knowledge of this issue. To fill this gap, the current study aims to analyze video gaming habits in children and adolescents during the lockdown, starting in March 2020 in Italy, the first European country affected by the pandemic. Specifically, we aim to understand how variables related to parents—for instance, knowledge of their offspring’s life, the monitoring of their video gaming habits, and parental use of video games—are related to their offspring’s time spent on video games and GD symptoms. A web-based survey involving parents (n = 554, 79% mothers, mean age = 45.39) of 554 children and adolescents (73% males, mean age = 11.11) was utilized. The results showed that they were involved in video games, particularly boys and adolescents, with high rates of GD symptoms. The parents also spent a considerable amount of time playing video games. A path model that explained the mechanisms through which parental variables were related to their offspring’s time spent on video games and GD symptoms, controlling for gender and age, was verified. Overall, the findings indicate the importance of educating parents to behave effectively with respect to video games and monitor their offspring’s video gaming habits.