As of 2023, education surrounding game design has become a fixture in university education systems around the world. As the teaching of game design is an inherently interdisciplinary subject with many connections to the arts and humanities, there are a diverse range of perspectives as to what the focus of each curriculum should include. In this essay, we argue that game programs with a more technical focus should include both design and play-focused approaches embedded into the pedagogy. We present two case studies drawing from our education journeys studying games as well as our experiences teaching in both game and computer science programs, and discuss the resulting benefits of integrating these concepts into our practice.