Quick terminology: generally, a striking tool with a head made from wood is referred to as a "mallet;" "hammers" used to mean just striking tools with heads made from metal (steel, brass, etc.), but it got confusing when plastic happened. Plastic-headed striking tools are called hammers or mallets, with no obvious (to me) pattern to when one term or the other is used, although the ones designed for use with wood-handled chisels (e.g., carving chisels) are usually called mallets.
That's a right interesting tool. I have no idea what particular purpose it was designed for. Is there any kind of maker's mark on it?