If air is moving through the engines, then it's providing thrust, which will provide forward movement of the aircraft because the wheels are FREE-SPINNING...

The problem didn't say the conveyor was moving at the same speed as the engines are rotating. It says it's moving at the same speed the aircraft will move. Again, the aircraft movement is measured by air going into a tube. If no physical movment of the aircraft, then no air going into tube, which means no movement of conveyor. If conveyor moves, then that means air is going into tube which means aircraft is physically moving (the conveyor movement is directly proportional to the aircraft physically moving), which means it will take off once it reaches the speed necessary.