This was probably not an attempt to set a record. It was rather to demonstrate what the new SAR helicopter is capable of. Perhaps also to show the flag in this remote location. This was a civilian MOJ helicopter but operated by the Air Force, visiting the military base on the island.
If you look at the map, Jan Mayen is located in the northwestern part of the Norwegian sea at 71°N 8°30' W. One thing is the leg out (and home), about 475 nm one way from the nearest airport in Norway. Another is alternates, the nearest is about 270 nm on the east coast of Greenland, the next 320 nm on the north coast of Iceland. That is relevant in this fog ridden sea area (25-30% of days with fog reported) and unreliable weather forcasts.