Technically in Iceland they are Huldufolk ("Hidden People") and they form a significant part of the lore of of the Icelandic people. Lots of people still believe in them, and if you want to look into why go here.
I am more interested in the not so subtle mocking going on in all of the articles about the moved stone. This is one of those areas where Materialists can say "Idiots!" and lots of Religious people can go "Heathens!" and they can both have a good laugh about it before they start bashing each other again.
Human history is long and broad and deep and is filled with people who believe in the existence of other intelligences. They call them lots of things: elves, trolls, spirits, fey, ghosts, demons, angels, aliens, jinn, kami, big foot, or ultraterrestrials of whatever stripe. It is in the Koran. It is in the Bible. It is in Buddhism. It is in the Torah. Shintoism is entirely about such beings.
All of our grandmothers (OK most of our grandmothers) knew and told us there were other things in the world than what we could see and feel. Even if they had stopped believing when they told us.
Stories told by countless people in countless places have so many striking notes of similarity.
My point is not to get you to believe in any of it. My point is that if you choose to dismiss outright the existence of such beings in general you are not being scientific or rational. You are acting on faith in your understanding of the world. A scientific answer would be "People have reported a phenomena. We do not have sufficient evidence to confirm or deny their conclusions about the nature of that phenomena. We must look at it further." And if people who were honest about being real scientists were in charge of budgets and grants there might be more research that was not considered "fringe."
If, as a religious person, you dismiss such things because they do not fit your cosmology I would suggest that you revisit your religious texts and traditions.
If we are to be honest, intelligent, people about matters of faith and science we cannot dismiss out of hand any phenomena that a lot of people claim to experience. We might reject in specific, but we should not simply do so as a default. That says that somehow other people's perceptions and reason are inferior to our own. It is not respectful of other people and it is not wise.
There is more in heaven and earth than dreamed of in your philosophy...
so occasionally think of the elves.