It gets as far as allowing me to finish creating/selecting a pirate then right after it finishes the little cutscene when it's about to load the island, the game just crashes to desktop.

So I found a solution thanks to a helpful person on Steam.

In the Install Directory open
Tropico2.ini

Find
[DDraw]

Change
SoftwareDevice=0
to
SoftwareDevice=1

Problem solved, GoG please include patch.

GOG already provides a patch for this. Take a look in the game's installation folder, there is a file called "Tropico 2 Safe Mode.bat". It uses the settings stored in Tropico2Safe.ini (including SoftwareDevice=1) instead of Tropico2.ini
Simply start the game with this batch file instead of the standard shortcut.