1) Parkinsonian tremor is typically at rest or with distraction. When you actually engage in purposeful action, such as using a spoon, the tremor usually dampens or goes away.
2) The main problem in Parkinson's is actually "bradykinesia" or slowness of movement. A more accurate term, in my opinion, is slowness of motor planning, that is, the brain systems cannot process the information require to, and then generate, a plan of movement for the limbs fast enough. The spoon won't fix that.
3) Parkinsonian and other forms of tremor do have relatively safe and effective treatments in medications or deep brain stimulation implantation.
My thoughts are - this spoon, if it works and isn't a mechanical nightmare, would be useful in a limited subset of cases where the tremor resembles another condition known as essential tremor, where the tremor instead is an intention or action tremor, where purposeful activity amplifies the tremor. Even so, these would only be in those patients who cannot get deep brain stimulation surgery for some reason. The reason being that DBS, while brain surgery, once done, is the more elegant solution. I.e. your tremor goes away, rather than requiring a superficial "hack" like this spoon.