May a LEGO Mindstorm NTX be controlled by a device using an app to control movement such as an iPad, iPhone, or iPod. Would the device be considered to be remotely controlling the robot through radio waves?

Yes, as long as the device uses one of the frequencies allowed in the rules as outlined on the NSO website, that would comply with the remote control through radio waves. However, be careful of the device used, it must not allow control or aid from sources outside the competitors.