The main reason that I would think it would be necessary to change the control board and tread belt is if they were damaged in some way. The fact that the motor malfunctioned does not necessarily mean the other two components are also faulty. Do you see any visible signs of damage to the belt and control board? If not, they do not need to be changed.
One other school of thought is that the control board may have become defective, leading to the motor burning out. In that case, a new control board would be recommended. Since you already changed the motor, start up the treadmill and see how it operates. If the motor does not burn up again, it means that the control board is okay, and if you have not lost performance from the unit the tread belt is also okay.