I could be wrong, but I remember reading that he owns a few car dealerships in Norway, and that his family was pretty wealthy. I also read a Swedish translation a few weeks ago that quoted him saying that term was a lot more important to him than the cap-hit. But I'm not sure if that report was one of those typical translations that gets taken out of context.
He does not own a cardealership :p He has Subaru as his private sponsor, who will supply him with a car to drive around in New York and Norway.
His family are working class people, not wealthy by any standard, medium income, pretty standard family by Norwegian standards.
There is a Zuccarello AS (Norwegian version of Co) that is ran part time by his mother, with a positive balance of around $84,000, probably from sale of merchandise and the like, plus private sponsors.
You are right that term is supposedly more important indeed, but the open question is what his agents who are currently dealing with management, have adviced him to do with regards to his current offer.
The worry is ofc that the Rangers brass wont be willing to go for more than 1 or 2 years, or are offering something under 3 mill, just to make things difficult