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I think the idea that Greece ruled the world is a bit of a modern fallacy; I don't really even think the word 'empire' is appropriate for describing classical Greece. Alexander the Great conquered a lot of land, but the entire thing fell apart within a couple of generations and the infrastructure to sustain a lasting Greek empire anywhere outside of Greece, Asia Minor, and assorted Mediterranean islands never existed. The Greeks left a cultural legacy that was sort of picked up and adopted by the Romans, who obviously went on to rule over a vast and rather centralized (for the times) state, so maybe that is where this misconception comes in. Hard to say.

Not to mention that they (the Greeks) were usually way too busy fighting with each other to concern themselves with foreign conquests.

To answer the second part of your question, Greece is a tiny, rocky country that is resource poor. This was as true during the height of Classical Greece as it is now, and served as the impetus for Greek colonization all over the Med (Siciliy, Southern Italy, Hispania... even North Africa), but it shouldn't be confused that this colonization was some kind of massive collective effort by the Greeks. You might analogize it to European immigration to the US --- people came from all over the place for many reasons but it wasn't a coordinated effort, it was driven by individual or regional factors in many different places.