In the Three-Age System, the defining characteristic of the Bronze Age that earlier ages didn't have was the beginnings of urban civilisation.
This happens to coincide with bronze and copper technology, hence the metal-based classification of "Bronze". In practice the really interesting part of a game or book exploring the Bronze Age isn't the metal in use* but the emerging cultures that straddled the boundary of what we perceive as hunter/gatherer and modern civilisation.
This shift shows up in the topics of ancient Greek poems (Proto-Orion, Centaurs) and the initial Judaic antagonism to city-states (Gomorrah, etc).
If you would like to get the feel of a video game exploring the Bronze Age, try UnReal World.
The games defines itself as late-Iron Age as this is the maximum technological era a character can participate in, but a character can also be anything from a Neolithic hunter/gather onwards. So Bronze Age characters and communities exist among the co-mingled settlement on the game's world map. The game is old graphics-wise but has been in continuous development for decades.
* Bronze: Easier to work. Iron: Easier to find