The possibilities of stem cell research helping patients with Huntington's is about the same as for Parkinson's. Although it's doubtful that HD specific research will be done (HD is so rare, research dollars are just not in great supply compared to other diseases) there is a "blanket" effect, and what benefits one neurological disease will benefit in some way, at least, another. The promise with stem cells is in growing new neurons, or brain cells. Since neurons die with HD, as well as other diseases, the research promises hope for everyone afflicted with such a disease. It could conceivably reverse damage, after a cure (and a way to prevent further damage) is found.
So when you read "Parkinson's", think HD, or Alzheimer's, or ALS. Many news organizations, when reporting the benefits, simply mention Parkinson's because so many are familiar with that one.