What is emotional benefit of an elderly person seeing a beloved grandchild far away on skype? Has anyone done studies? What are your thoughts?

Probably a lot. When distance is a barrier a face and a voice do very well at making a good connection emotionally. After all, what is the first thing we have access to as we are introduced into this world? Yes! a voice and a face! i would guess that common sense says the benefits are great. If there are studies I am unaware of them.
Connectedness Is Key. As human beings, we need to feel connected to others. While some would argue that skype is not as good as playing cards together, it is better than nothing &, i would be willing to bet, better than phone calls.