Rock-paper-scissors type randomizers
Race for the Galaxy has this kind of randomness in the action selection phase, although it has a lot of luck of the draw in it as well.  A typical early game example is the explore, settle, trade relationship in the early game.  Often, you want to explore if other players trade, settle if they explore, and trade if they settle.

On the other hand, I disagree that this is not inherently lucky.  If we play Rock Paper Scissors, and I play uniformly at random, the only way that you are going to beat me is luck.  Even if we introduce a little bit of information into the game, if I am making a decision that has any randomness in it, and I certainly should be if the game can be reduced to a mixed strategy, then the game still has some luck involved.