But beyond these two civilizations, the wider Mediterranean has plenty of material. This post is a snapshot of bits and pieces of things I've found in my amateur research.
The Cradle of Empires, A Melting Pot
Ancient Greece and Rome, the Byzantines, the Ottomans, Egyptian dynasties, Babylonia, Persia...countless renowned civilizations touched its waters, their legacies still standing in the forms of pyramids and architectural wonders. And perhaps more familiar to gamers, southern France and Spain touched its borders as well, and even the non-native Mongol Empire reached its eastern extremities as they sacked the Middle East.
Related to the previous entry, the diversity of civilizations in the Mediterranean provide a prime opportunity for taking fantasy counterpart cultures while retaining an authentic atmosphere. Arabian Nights-style fantasy, glorious pseudo-Roman metropolises, pyramids housing undead lords, feuding merchant houses in Vencian city-states, Slavic-style Balkan villages, and all the monsters and folklore of such cultures would make for a populous and interesting world for fantasy gaming.
Additionally, the sea as a central location would allow for the GM to let the PCs traverse uneventfully from one realm to another instead of worrying about buffer states and or glossing over the intervening lands ("no no, in order to get to the Sultanate of Kremdora you'll need to traverse the Dragonlands first, and that's if you manage to make it out of the Dire Desert, and then we can have adventures there").
Mobile War Altars
The Carrocio, or war altar, was an iconic possession of medieval Italian cities. Its use was to boost morale, displaying the city's coat of arms as priests gave sermons and trumpeters encouraged soldiers to battle. Each Carrocio was the pride and joy of its people, and for the enemy to seize it was considered a major defeat no matter the eventual outcome.
How can this be adopted for fantasy gaming? Perhaps the Carrocio has magic powers, capable of boosting bardic music and divine spells as long as the person standing upon it gives a good performance or sermon. Extending the range of such abilities to many soldiers would make this a coveted prize for any army, thus explaining their high priority.
Armor-breaking Swords and Damascus Steel
The flyssa is a sword which was popular in use among the Berber (Amazigh) tribes of North Africa. The blade was specifically designed to break open chainmail armor, a common means of defense in that region of the world.
Additionally, the city of Damascus in what is now modern-day Syria was known for its namesake Damascus Steel. This material was used in the creation of distinctive swords notable for aesthetic patterns similar in design to flowing water. The secrets of their creation died with the artisans, and to this day modern engineers can only theorize as to the techniques used. All the same, its high quality gave rise to many legends, such as the ability to cleanly cut through a rifle barrel and finely split a strand of hair.
In fantasy gaming, flyssa swords might provide a bonus for the purposes of sundering armor, a technique normally reserved for maces and other blunt weapons. A secret society of artisans using Damascus-style Steel might be able to create unique magical swords.
A Turkish Subterranean City
Derinkuyu was a multi-level underground city in the ancient world capable of holding as many as 20,000 people within its confines. Not only could the front gates be closed off via stone doors, each level was capable of cutting itself off from the above levels in a similar manner. Schools, stables, cellars, chapels, and other urban accommodations were believed to be present. The city was used for protecting the populace from invaders several times during the Byzantine reign.
I might expand further on the region, including specific entries for fantasy counterpart cultures such as Egypt, Mongol armies, the Balkan Mountains, and others once I do enough research. All the same, I hope I wet your whistle in the potential the Mediterranean has for fantasy RPGs!