Why does RollerCoaster Tycoon (original) on Windows 7 display a black screen on launch?

The solution was to disable 3D acceleration in VMWare by unchecking the "Accelerate 3D Graphics" under Settings... options for the virtual machine.

This solved the issue not only for the 2010 Mac Mini, but also for a 2011 27" iMac.

This solved the issue not only for Roller Coaster Tycoon (original), but also with Corkscrew Follies, and the Deluxe edition.