There are many games that feature power struggles, war, and strategical maneuvering, and these all carry political connotations and even ramifications. Chess comes to mind as a qualifier in this category, for it is all about strategy and was originally based on war, but let's look at a few other possibilities.
We might think of the board game Risk, which is all about empire building. The Civilization series of video games is also based on empire building, as is Stellaris, which takes diplomacy and empire to a universal level, literally.
For people interested in World War II history and politics, Axis & Allies comes to mind along with Conflict of Heroes. Games focusing on other historical eras are plentiful as well, including Ultimate General: Civil War and Grand Tactician: The Civil War (1861–1865). All of these carry political connotations, for politics is at the heart of war, and players are required to recognize political motives and make political decisions in game play.
Finally, there is a whole class of political simulation games available. These include Democracy 4, Power & Revolution, Superpower 2, and Rogue State. All of these allow players to try to cope with the powers and conflicts of ruling a nation.