If I'm Laine I'd prefer to sign for at least 2 years because a 1 year deal just gets me traded. And while UFA often means a bigger payday, I don't think it does in this case. Maybe Laine thinks it does but I don't. I don't think there is a GM in the league that values him higher than Jarmo does. If he gets traded then that takes away potentially his highest bidder (Jarmo) and takes him away from a strong situation with a coach he can work with and now an A+ playmaker that can pump up his value. If he's traded he loses all of that, and if he stumbles next year he's looking at a paycut not a raise.
If Jarmo was Laine's highest bidder the contract would be signed already.
Not specific to Laine, but as a player I would never agree on a 2 year deal in his shoes. There are no guarantees that he won't be shipped immediately to Arizona after signing the deal. Any NTC/NMC he signs will take place no sooner than a year from now and he could be Jeff Cartered to Arizona or any other undesirable location. Both Marian Hossa and Devin Setoguchi were traded within a week of signing their 3 year contracts and Carter as we all know was traded just before his NTC was about to kick in. Justa week ago Vanacek was traded a day before his wedding. Toronto bought out the last 4 years from Grabovski's contract a day before his wedding day. Only a fool of player trusts a GM to have his back.
One year deal would give Laine the leverage against Jarmo. Laine has already made it crystal clear that he wants to stay. For Columbus there's no risk except if Jarmo is not serious in his offer. Getting traded would not be the end of the world. He still gets to choose his next team. Maybe play in Florida with his best buddy Barkov, follow in the footsteps of Teemu and join the up and coming Ducks or choose the Hossa route and sign a 1 year deal with a real contender for a chance to win the cup. Or simply choose highest bidder (Kraken).
Laine is also not the type to worry about a paycut. He is too confident to worry about stumbling next year no matter where he ends up.