I could well be wrong here (please correct me if I am).
Wasn't Old Norse divided into Eastern and Western? With Icelandic and Faroese related to Western Old Norse whilst Swedish descends from Eastern. This would imply that Älvdalska would be related to Eastern Old Norse - hence not totally unique but still of great interest.
Nowadays we have nation states and boundaries. We have a buraucracy, publishers and broadcasters located in the capital that influence the language spoken in that country. 500, 1000, 1500 years ago it wasn't quite like that. Things were more fluid.
Älvalska descends from whatever was spoken there, which was presumably closer to what was spoken in Uppsala at the time than to whatever was spoken in Hamar (in Norway some way west of Älvdalen). But there wasn't a ban on travel to Hamar, nor a state that lent prestige to the dialect spoken in the capital.
I've only had a few courses about Old Norse, that were mainly about Old West Norse, so I'm not really an expert in this topic. I think we pretty much know the differences between Old Western Norse and Old Eastern Norse through the texts of that languages that were preserved.