The fix is pretty simple: in the folder where you've extracted / install Aptana Studio 3, you should have a file called "AptanaStudio3.ini" - open this file with a text editor and at the end of the file, add this line:
-Dorg.eclipse.swt.browser.DefaultType=mozilla
That's it. Using this fix, Aptana Studio 3 now works properly on my Ubuntu 14.04 machine.