There's a few things at work here.
1. The coexistence of the terms Diocese and Prelacy is really only relevant in North and South America. The term "Prelacy" is predominantly used to refer to dioceses under the authority of the Catholicosate of Cilicia. As I understand it, Cilicia has historically overseen the Armenian Church in the general Mideast, which is most of what you see on that list. "Diocese" is used for dioceses under control of the Catholicosate of Etchmiadzin. It's an issue of how it's translated into English, really.
2. It was not until the mid 1950's (1956?) that Cilicia had formal prelacies in North America. Though there was an informal break as early as the 1930's, prelacy parishes did not formally go under Cilician control until then. Hence, in the United States and Canada, there are Eastern and Western Diocese and Prelacies, and a Diocese and Prelacy for Canada. Many communities have two churches, often within sight of each other. It's that kind of thing.
3. Michal, in regards to your question. No. Cilicia does not "have" the Americas and Greece. Cilicia, as I said, did not really have an administrative presence in the United States and Canada until the 50s. There is no arrangement between the two over who controls which part of the world, only parallel jurisdictions if both have been established. There are no Prelacy parishes in Armenia, and there are no Diocese churches in the Middle East.
4. It's a little complicated to explain, and a bit outside my pay grade, but to start with the patriarchates. The Patriarchates of Jerusalem and Constantinople look over very specific territories, and are essentially autonomous to themselves, though both recognize the primacy of Etchmiadzin. In fact, the title of Patriarch isn't really much more than an official role held by an archbishop. Jerusalem oversees the Armenian presence in the Holy Land. Constantinople oversees the Armenian presence in Turkey, predominantly Istanbul. Each maintains the primacy of Etchmiadzin.
The Catholicosates are a bit more complex, but each have their historical role. Cilicia maintains that they are an equal Catholicosate to Etchmiadzin, while Etchmiadzin sees themselves as the Catholicosate of All Armenians, including Cilicia. It's a bit of a sore subject, and I'm trying to be as diplomatic about it as possible, but there are historical issues going back hundreds of years that constitute the positions of both. And a pile of political issues that are relevant today.
I hope I'm explaining that in a clear way. The organizational structure of the Armenian Church is complex to say the least.
Here's the website for Etchmiadzin, by the way.http://www.armenianchurch.org/