However their island is somewhat reliant on import (e.g. if you need wood to build something, there is no really useful amount of wood growing there). That means export is really important. And that for many people means fishery.
I could imagine that many young people in Reykjavík have a different experience as many of them can earn a living selling online services internationally.
As a EU citizen I don't see this as a Brexit-like event, it is clear that our Icelandic friends are EU-friendly and aligned with many of our laws and regulations already. The fact that they don't want in does not change that there are existing deep ties to the continent.
(This was an option for the UK, and is actually pretty much what a lot of the yes campaign was pushing, but is very much not where the UK ended up.)