In fact, the only in-app purchases in the game are content packs that bring you the "Time Twister" and "Wacky Worlds" expansions from RCT2 for $2 each, as well as a ToolKit that equips you with a Park Scenario Editor, Ride Designer, and the ability to import/export your parks from your friends and from RCT2 on PC if you still have those files lying around for some reason (another $6). All said, you'll have to drop $16 to fully unlock the game.
Here's how Atari describes the game on the App Store:
"RollerCoaster Tycoon Classic is a new RCT experience, combining the best features from two of the most successful and beloved RCT games in the series’ history -- RollerCoaster Tycoon and RollerCoaster Tycoon 2.
Create and run amazing parks complete with the most outrageous rides imaginable. RCT Classic includes a mixture of authentic playability, depth of gameplay and unique graphical style of Chris Sawyer’s original best-selling RollerCoaster Tycoon PC Games, now enhanced for handheld devices."