In this study, we develop and test a board game to introduce quantum computing to engineering students. The instructional approach is informed by peer instruction and flow theory. To begin, Bloom's taxonomy is leveraged to profile the intended learning outcomes (ILO's) from a master's course in Quantum Information. This is followed by a filtering exercise to shortlist the ILO's that are deemed suitable for our intended audience and for use in a boardgame. Design thinking informs the design methodology. The game, "States & Gates," is differentiated from other similar offerings in that it is designed specifically for a technical audience where, for example, it leverages matrix multiplication as a game mechanic. For product testing, a feedback form is used to evaluate the design and instructional value of the product. The goal is to identify from what/whom the players learn, alongside questions about perceived aesthetics, usability and sentiment. The feedback suggests that peer instruction is a critical pedagogic aspect of playing the game, and that this form of instruction is most effective for players who identify as being novice, but not entirely new to the subject. Further, several suggestions for product improvement were offered that warrant the development of augmented digital features. The game was developed as a tool for the community and is available for download at our GitHub repository.