Self-Determination Theory (SDT), a major psychological theory of human motivation, has become increasingly popular in Human-Computer Interaction (HCI) research on games and play. However, it remains unclear how SDT has advanced HCI games research, or how HCI games scholars engage with the theory. We reviewed 110 CHI and CHI PLAY papers that cited SDT to gain a better understanding of the ways the theory has contributed to HCI games research. We find that SDT, and in particular, the concepts of need satisfaction and intrinsic motivation, have been widely applied to analyse the player experience and inform game design. Despite the popularity of SDT-based measures, however, prominent core concepts and mini-theories are rarely considered explicitly, and few papers engage with SDT beyond descriptive accounts. We highlight conceptual gaps at the intersection of SDT and HCI games research, and identify opportunities for SDT propositions, concepts, and measures to more productively inform future work.