Looking at my board game shelf right now, a few that have some class implications:
Twilight struggle - Play through the cold war. Incredibly fun but complicated.
Carcassone - a battle between feudal lords trying to capture as much of the commons as possible.
Jaipur - Ruthless trading about buying as cheaply as possible, and selling for as much as possible.
Ticket to ride - Railroad monopoly titans fighting over limited terrain.
Risk - Napoleonic warfare, but IMO the capturing of countries and continents gaining you more soldiers each round, implies industrialization and colonialism. Axis and allies kinda the same deal.
Pass the pigs - Do I need to elaborate on this one.