Walking poles certainly do take the pressure off the knees. Personally, I use them on steep descents or unstable surfaces while hiking (although I tend to fold them away as being more trouble that they are worth on level ground.
Most poles are so light that the extra calorie burn is minimal. Certainly, they can help you walk faster in some conditions, which is where the claims of additional calorie burn have some legitimacy. But it is the WALKING that is burning the calories, not the arm movement.
If the poles are helping you walk further or faster than you otherwise could (especially with arthritis), then that is great. But there is nothing magical about the arm movement.