Hello! I am looking into running this game as I have played it quite a bit casually. However, I have one question. How do I know when I get Superstar Player? Do I have to count the number of games that I play? Or is there something else? Any answer would be appreciated!!!!

Monita will let you know when you exit the game, and a star will appear above the game. If you want to know how many games you've played so you can stop, yes, you'd need to count.

To follow up on what JBMagination said, you can press Y (I think) to select the games from a menu as opposed to having to walk to the gates. You can see which attractions you have a star on at a glance from there, as there will be a star in the top corner of the card representing the game.