My first impression, which was shared by a friend who hasn't gamed in ears, is that it smelled like MtG card circa the Mirage expansion. This lead to a long, drunken conversation about how strongly we associate memories with the distinct smells of new NES cartridges, TSR-era books, and Marvel comics.
However, I asked my wife, who has a much more acute sense of smell than I. She assures me it's the plastic pouch the dice come in. In other words, the box has a slight odor of cheap plastic.