Although co-designing games has received ample attention from researchers, there is a research gap on intergenerational co-design of games with children and young people where children’s unconstrained ideas are the basis for game co-design. This is particularly important when co-designed games are aimed at children. We explored a co-design process of digital games involving 4-year-old children, high school students, and college students in Joensuu, Finland, during October–November 2020. Over the course of three co-design workshops, six kindergarteners (3 girls, 3 boys) played freely with building blocks while six high school students (3 females, 3 males) observed their play, asked questions to the children, and interpreted the data to design two digital games. These designs were further elaborated in co-design meetings between the high school students and college students (12 males, 1 female), latter of whom developed mobile games based on the designs. In the fourth workshop, the kindergarten children tested the games. We used qualitative content analysis on the data collected via interviews of the high school students and observations of the co-design process. The outcomes of the co-design process were the conceptualizations and game designs by the high school students based on the children’s play, and the implemented games by the college students. The participants’ intertwined creativity, thinking and content production were observable in the games. Based on the interview data analysis and our observations, we identified unique contributions and assets for each group. Furthermore, the high school students’ interviews revealed 28 success factors of the intergenerational co-design process. Based on these findings, we present a generalized representation of the intergenerational co-design process that can be used for planning intergenerational game co-design projects involving young children and older age groups.