Scientific skepticism is your friend. The only thing this ball can offer is a bit of resistance in the form of gyroscopic action. In what manner could a resistance exercise "prevent sore wrists and elbows from boxing?" There is no magical process radiating from the flywheel, and that means that this ball can only accomplish the same results that comparable resistance exercises can.
If your workout regimen leaves you with joint soreness which falls outside the norm for exercise of that intensity and duration, you should consult a physician.
If something seems too good to be true, it almost certainly is.
Edit: If you are looking for exercise tools/exercises to strengthen your hands, wrists, elbows, and shoulders, I would strongly recommend that you look into some of the tried-and-true free weight options. I personally benefit from training with weighted Indian clubs, maces, and kettlebells. There are several exercises with these training aides which strongly benefit joint rotation and strengthening. These types of weights are relatively inexpensive, and have a broad utility in training the upper body.