Well to score goals a player needs to possess the puck and be in a scoring position. There are territorial battles for ice position and there are intense battles for loose pucks. It doesn't matter how skilled a player is if they can't battle for loose pucks, steal pucks, retrieve them in the corner and battle for position. All of the successful skill players are capable at doing that. They aren't knocked off the puck easily. They win races to loose pucks and can out battle other players to retrieve the puck or to get into good positions. They win because the out compete their opponents.
It is the whole dog fight saying. It isn't the size of the dog in the fight, it is the size of the fight in the dog. Players both big and small will be beat by players who have more fight in them and are willing to battle harder. Skill players that are successful don't shy away from the dirty areas.
Elite skill with elite compete level is the most desirable combination. Skill without compete doesn't end up being very helpful in the playoffs.