I finally installed Mountain Lion yesterday and found a quick (but hopefully temporary) fix to enable my application to run on it. I actually didn’t change the application, only the way it is started. You can download this additional package here. If it works as planned, it should successfully start the WiimoteWhiteboard application that you have already installed.
Please note that this is experimental and couldn’t fully be tested since I don’t have a Wiimote with me at the moment. Hence, please do let me know if this works for you.