The GOG.com shortcut uses an application which sets the game's affinity to two cores to avoid choppy music playback. If you launch the executable without using the shortcut (for instance, when launching the game via a trainer's window) you will have to manually set the application's affinity with two cores while the game is running.
To do so you must switch to your desktop by using the Windows Key or Alt-Tab or Ctrl-Esc. Now enter the Task Manager by right-clicking on your start menu bar and selecting "Task Manager". Find EarthwormJim3D.exe on the list, right-click it and select "Set Affinity...". In the newly opened window make sure two cores (i.e. CPU 0, CPU 1) are checked. Click OK and close the Task Manager. Click the Earthworm Jim 3D button on the Start Menu bar to return to the game.
It is possible that the game's fonts will appear distorted after returning from the desktop. Starting a game or switching to a different menu should refresh the fonts displayed and fix this problem.