If your school focuses on intrinsic motivation, then I would think the students are accustomed to the concept of winning for the sake of knowing they did their best and had a great day, and not neccessarily for a prize. So, you can still utilize the scoreboard game simply for the game itself. Big, fun, mighty cheers and the satisfaction of seeing how well they've done throughout the day may be all it takes if they are accustomed to pure, intrinsic reward. In addition, you can look at some of the academic games as goals for them to work toward. Pose it to them not as a 'prize' but as a 'goal'. Explain that if we use our time wisely, then we have time to play...you can use super-speed, crazy professor, beach-ball baffler, and mind soccer as academic games. You are increasing fluency and/or reviewing class material and they are having a BLAST doing it. If they win, it is a sign to everyone that the class has used their time wisely, so you then say, "Well look at that...now we have time for _______." It demonstrates for them the benefits of using time wisely...you have more time for the activities you enjoy.

I'd love to hear more on how this goes for you, I think it's an intriguing topic to work into our Whole Brain Teaching discussions.