The mapping here could be improved. At the moment the whole park is mapped as a leisure=park and a tourism=theme_park.

The park itself is free if you arrive on foot or by bike. You can then hike up the mountain, use the trails, picnic areas, etc.
If you come by car you have to pay for parking.

And then there are ticketed attractions. The tickets can be bought at the "ticket plaza", that is roughly where this note is if I remember correctly. There is a small area with restaurants that is only accessible to ticket holders, you cannot go there without buying a ticket for the attractions. 

Maybe it would be better to have the whole park as leisure=park and then the area for ticket holders only as tourism=theme_park? Unfortunately this would require another survey, I am not sure what exactly the boundaries of this area are.