Make sure the game and/or installer aren't running, then in the Finder, press the Command-Shift-G keys and paste the following into the “Go” field:
~/Library/Preferences/Command and Conquer - Red Alert 3 Preferences
When the "Command and Conquer - Red Alert 3 Preferences" Finder window opens, move the contents of the folder to the Trash, then restart the game.
When the game finally starts and you see the main menu, press Command+Return to go into windowed mode. Then change the game’s screen resolution to what you want it to be in the Options. Finally, press Command+Return, again, to go back into full screen.
I think the root of the problem is that it's an older game and has problems with the way Mavericks handles an app in "full screen."