Technological advancement has seen a rise in computer-based and online gaming, and the online space has facilitated a proliferation in gambling options that increasingly adopt game-like features. There is a concern that gaming in childhood could predispose subsequent engagement with gambling behaviors, which has drawn the attention of parents, researchers, governments, and the European Union. To inform policy and legislation aimed at mitigating gambling-related harms, this research uses three waves of longitudinal data from Ireland to examine whether computer game engagement at 9-years-old (collected in 2007/8), and online gaming at 17 and 20, is associated with gambling participation in young adulthood. Multiple regression models, adjusting for a range of socio-economic and health characteristics, revealed that online gaming at 17 was associated with 1.4 higher odds of more frequent online gambling at 20 years (p = 0.011), while online gaming at 20 was associated with a 1.7 higher odds (p < 0.001). However, no association between early computer-based gaming at 9 years and subsequent gambling behaviors at 20 was uncovered for this cohort (born in 1998). Given more recent introductions of loot boxes and social casino games, continuous research is needed for future cohorts which may be greater affected by such developments.