They must play the activities at least once to get a stamp. As they get the stamps, the others are unlocked. After unlocking the areas, then they need to get all the stamps. Once that is finished, then they must get keys to unlock the items for their villas. Two types of keys exist: silver, where they need to play the games throughly (1P only, sadly), and gold, for completing various objectives within the worlds... and some trivial objectives exist too, like driving into water holes 50x, falling off cliffs 50x, etc.