Preliminary note: the search for the cause of a widespread and complex cultural phenomenon is nearly always doomed. For whatever it's worth, I encourage you to be skeptical of anyone that claims that they know the reason for any broad and rich cultural movement.

That being said, two clusters of explanations come to mind as offering some reasons in this case. First, there are reasons extrinsic to Greek culture. Greek intellectual culture happened to become the progenitor of our own. This may have partly been due to the merit of Greek ideas, but it was also partly due to factors completely disconnected from that (such as the contingent historical fact that the Romans were deeply influenced by Greek culture and happened to also play a pivotal and lasting role in the formation of later cultures). Had there been equally complex philosophical thought among, say, the Ligurians or Dacians, it simply would not have been transmitted to modern Western thought as faithfully (if at all), and certainly would have had little chance of becoming part of the way we do philosophy today. We are all looking at Greek ideas today through a lens given to us by the Greeks.

But I take it that you're particularly interested in reasons intrinsic to Greek culture. There are some, but these are complicated. The Greek city-states leading up to the birth of philosophy enjoyed a measure of cultural unity (through Homer and Hesiod) and linguistic unity (through a collection of mostly inter-intelligible dialects) while also enjoying political disunity. Contra your own wording, they certainly did not constitute an empire (until later, and then only briefly). This meant that neighboring communities, with whom one might converse and whom one might culturally understand, did things very differently, politically. This arrangement affords good grounds for comparative and critical thinking about alternative approaches (I'm no expert, but I understand that similar cultural-unity and political-disunity combinations are demonstrated by the Italian republics of the 14th century, the warring states period in China, and northern India in the late Vedic period--each of which have accompanying bursts of intellectual activity).

Another reason intrinsic to Greek culture is the Greek development of a written script with a phonetic character set. That is, the Greeks used one mark to represent each sound, rather than each syllable or idea. One consequence of this was that a Greek speaker could write down a word or name from another language, even if it used syllables (or ideas, for that matter) that the Greek language didn't use. The written foreign word or name could then be read (albeit approximately) by other Greek speakers who did not know the foreign language. This equipped Greeks to communicate about ideas from other cultures with whom they had contact, in a way that was precluded (or at least much more difficult) for those who spoke a language that had only a syllabary, consonantal, or ideographic script (though these have other advantages, of course, over a phonetic script).

Sources: Mark Munn has an excellent book on 5th-4th century Athens in particular, The School of History: Athens in the Age of Socrates. Of course, for my money, there's nothing that beats Thucydides as a starting place for understanding the culture of 5th century Greece. If you're looking for big-picture claims about history that are a bit more grandiose and profound (and not always quite as rigorous), you might look at Jaspers' Origin and Goal of History. My favorite run-through of western intellectual history and philosophy is Anthony Kenny's Illustrated Brief History of Western Philosophy.

edit: a bit of grammar

Source: The Human Web by the McNeills

Basically, the reason why Philosophical thinking (and other advancements in literature, science, astronomy, etc) was allowed to occur in Greece was due to the general absence of an authoritative religious body (as this role was taken up by the Magistrate, who usually cared more about the materialistic side of government).

Because of this absence, there was no authoritative body that could suppress the philosophical ideas in question, most of which were quite secular, and thus Philosophy could develop and reach new levels of sophistication.

(edit to add conclusion)

It's entirely possible that people philosophised before the Greeks, but in the case of Greece there happened to be a lot of factors that allowed for a rich philosophical world to evolve.

Greece (especially Athens) was fairly stable (note: fairly) and there was a combination of cultural and social factors that allowed philosophy to take place. One of the most important of these was the fact that many of the philosophers (especially Plato and Aristotle) were wealthy. This meant that they had time to sit around and philosophise.

My wording is appalling, I'm sorry. I hope that helps a little, though.