After reading the course syllabus that they sent, I have to somewhat agree with Bored - in that it is very FAR based which means transfering that knowledge to the EU or Middle East will require further study than the course shows. While this is not difficult, it is something that you would need to take into account because while most of the major regulations are the same, there are regional differences (flight duty time, airspace configurations, etc) that become a pain when planning a flight, and that seems to be something they are not teaching by only going the FAR route.
However, I disagree with the need to work yourself from the bottom up in a single airline to become a dispatcher. All of the dispatchers I know have worked up through the industry from smaller operators to larger ones (just like Pilots), and by the time they reach the majors they have all the operational knowledge that a dispatcher needs, without ever having to have washed an airplane or do the things that, quite frankly, are useless for international operations.