Your are has high humidity in the summer, that is one reason the basement is damp. If you open the window, the warmer basement air can hold more moisture so it will feel drier, but as soon as the window is closed and the temperature drops due to the cool earth, the humidity level will go up. In other words, opening the window won't reduce the amount of moisture in the basement, just make it feel better. The dehumidifier both heats and dries the air in the summer with the window closed.