I think it's just a matter of a different type of competitiveness. Figure skaters, though they compete in competitions so technically against others skaters, really compete more against themselves and are constantly driven to improve.
Hockey players are too, to an extent. The difference is, as a hockey player, to beat another player all you really have to do is knock them down, or 'off the puck'. You don't always have to be better, you can just be tougher, smarter, a harder checker or have a more accurate shot.
In figure skating you quite simply have to be better than your competition or you lose.
Hockey players, as I started to say, physically compete against one another ( checking, shooting etc.) Figure skaters pretty well compete against themselves ( which is much harder imo).
If it makes you feel any better, there is an increasing amount of professional hockey players who use figure skating coaches to help them be more agile on the ice.