Achilles is playing a game with Ajax. Presumably, it's a gambling game. They're armed, though, and ready for battle. The photographer notes that this was a popular theme of the late 500s B.C.
Achilles and Ajax were both major heroes of the Greeks during the Trojan War. Both die during the war, Achilles by a divinely-guided arrow shot by the Trojan prince Paris into his Achilles' heel, and Ajax dies by suicide when he was driven mad by Athena to prevent the warrior from killing his fellow Greeks. The madness came after the decision to award the armor of the late Achilles to Odysseus, instead of Ajax, who wanted it and felt he had earned it.