You play to win, regardless, but I think fans should be rooting for wins especially in this case, given the circumstances.
This organization has many good young prospects, including three that are among the best leaguewide at the position, and two that may be generational talents.
More importantly, several of this teams prospects who will have to come together in the future anyways are already on this team. If this team isn't able to be relatively competitive, no Phil Kessel or Erik Johnson is going to change that drastically.
The coach and these players need to be focused on this season and building for the future with their core of young players. I'm not expecting or even hoping for a massive winning streak, but this team should be playing to win games and should be competitive every night.
They are going to end up with a high pick regardless, though, just because of where they are in the standings.