Got it, how stupid of me!
The original RCT didn't work properly on Windows XP, so they released a patch for it. Here's a working download for it.
To install the patch, follow these steps -
Step 1 - download the patch.
Step 2 - browse to your RollerCoaster Tycoon's Wineskin, which is located in your home folder > Applications > RollerCoaster Tycoon > "Show Package Contents" > Wineskin.
Step 3 - click Install Software.
Step 4 - click Choose Setup Executable.
Step 5 - select RCT-US.exe, which is the patch you downloaded.
Step 6 - install the patch like normal.
Yeah, you installed RollerCoaster Tycoon correctly, but since Wineskin is based around Windows XP, there was a bug.