Teachers who attempt pedagogical innovation with authentic digital games face significant challenges because such games instantiate open systems of learner activity, inviting enquiry learning rather than knowledge acquisition. However, school environments are normatively sanctioned cultural spaces where direct instruction and high-stakes tests are "de riguer". In this paper, we draw on the conceptual frame of dilemmatic spaces to illuminate the dilemmas teachers encounter when attempting to reconstruct professional practice in the classroom. We worked with nine teachers who enacted the "Statecraft X" social studies curriculum. Drawing on coded interview data, our findings suggest that teachers are forced to wrestle with tensions engendered by misalignments that emerge from the innovation's tacit requirement for change and the system's inherent gravitation towards maintaining the "status quo". A school culture that cultivates innovative practice based on greater teacher agency is needed for authentic game-based learning to find traction in the classroom.