Turns out that yes, each Attraction can earn a star, as explained in this video:
Basically the requirements are:
- Complete all "standard" levels for the Attraction (competitive modes and Extra levels don't count)
- Play each competitive attraction 30 times (win or lose)
Single Player Attractions
- Complete each Attractions "main game", since they're all arcade style games, this pretty much just requires you to play until the game ends. Some games have a second course, which doesn't count for the star. Unlocking the second course is usually enough to unlock the star, as well.
As a bonus, when you've earned all stars, you can see the credits (yay) and play a star shooting minigame (less sarcastic yay).