Your observation is correct and the caption is wrong. The round double-grip shield shows that this warrior is a Greek hoplite. He is wearing a cloak called a chlamys, fastened on one shoulder with a brooch. The Corinthian helmet with transverse crest may imply that he is meant to be an officer.

That said, the warrior's equipment includes several features that may actually be Roman. To my knowledge, there are no Greek examples of greaves decorated with animal heads (though there are some with faces on the knees). While linen cuirasses might feature a face of Medusa on the chest to ward off evil, this was not typically a feature of anatomical "muscle" cuirasses until the Roman period. Finally, while the picture doesn't show enough detail to be sure, the sword appears to be a Roman gladius rather than a Greek xiphos. It is a common error of artists and costume designers to make no distinction between these sword types.

Meanwhile, the little wristbands worn by the warrior in the picture are neither Greek nor Roman. They are a feature of modern Hollywood costume that has become so pervasive that, to most people, an ancient character now appears unrealistic without them.