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.