I really play games for those moments where you communicate with a player/players _on the other team_ through the meta. And then you dance around the strategies trying to set/catch each other offguard.
And you _know_ when you're playing against someone that gets it. And you can tell certain players apart, or classify their level of meta-ability by they way they're playing.
Sometimes in chess, you're embroiled in a really intense battle in one area of the board, but the game is developing on some other level and is primed for a swift turn, and knowing your opponent is aware of that same notion is really beautiful.
A great, quick and easy card/boardgame for revealing this kind of meta (but it's kinda one dimensional when you "get it") is "The Mind".
https://boardgamegeek.com/boardgame/244992/mind
It's great for giving people a taste of the thrill of meta.