The map lays out a region that is somewhat reminiscent of the Mediterranean, depicting an enclosed sea dotted with islands. The map already shows the location of various city states, so all the GM has to do is determine the nature of the states and the balance of power, etc. Most of the city states on the islands would be ancient Greek analogs, complete with fleets of triremes. You could add some mythological touches, like an Amazon city, etc. I would give the southern city states an ancient North African feel, while the northern ones would be more Celtic. I'd be tempted to change all of those ice hexes to savanna, but you could leave them as they are and put some faux-Vikings there. Mixing and matching historical societies is a staple of fantasy, after all.
"Your pickled herring or your life!"
The map also helpfully lists the location of Magic Items, which as Jeff suggests would be the campaign's dungeons. To fit the Bronze Age theme, I would take a RuneQuest-like approach and make them the ruins of ancient cities. Maybe some are the haunted ruins of a lost Atlantean colony, an abandoned Egyptian outpost, or Cyclopean ruins - literally the ruins of a cyclops city. For example, that one in hex 2122 would be some kind of spooky pyramid complex. Another feature of the map is the various aeries listed. These are intended to be Roc nests, but I would probably change them to griffin nests - or even dragon's dens.
With all of those sea hexes you're going to want some sailing rules. How you handle it depends on how detailed you want to get. The easiest way is to just have players make a skill roll (or the equivalent) whenever they have to deal with a storm or pursuing pirates. But I would even consider incorporating some navel wargames rules into the game. That depends a lot on the players and the "feel" of the game you're trying for.
Most fantasy rules would work for this with only a few cosmetic changes. If you want a game that already matches the setting the obvious choice is Mazes & Minotaurs. But really it's just a matter of taste.
Update: Two more rules options are RuneQuest Bronze Age Sourcebook (RQ3) or Runequest - Age of Ancients SRD (MRQ1).