The MFA catalogue says only this about the monster depicted:
A. Mayor has recently interpreted the head of the "dragon" as an image inspired by the sight of a fossil skull emerging from a cliff (see The First Fossil Hunters, Princeton, 2000, pages 157-165).
This article says:
Art scholars have generally interpreted the monster (yellow face at right) as a sea serpent emerging from a black cave, but Mayor and a group of paleontologists think the creature might actually be the fossil skull of an extinct giraffe eroding out of a hillside. Mayor's analysis of the vase painting appears in the February OXFORD JOURNAL OF ARCHAEOLOGY.
The monster does look more like a skull than a real dinosaur head to me. We would expect to find a lot of dinosaur remains if they lived as recently as 2500 years ago. If dinosaurs existed then, wouldn't there be a lot more depictions?