Ultimately, what is most important when teaching someone a game: how to play or how to win?

How to play. Winning will come when they understand the game.

How to play.

Well how to play of course.

If you teach the most important thing in the game is winning . . . You will have created a monster, that is incapable of enjoying the game itself. 

How to play. Learning how to win on your own means is the allure of the game. Plus, just teaching how to win without how to play in depth can lead to gaps in the learner's knowledge.

How to play.

"How to (gracefully) win" is best taught as a general life principal.  Along with "How to (gracefully) lose".

How to play 100% because how to win will come after the basics have been taught. Take Poker or Blackjack (my favs) for example, you need the basics and then you can learn how to win. Many other activities follow this same theory.

Hello! I suppose that you will have to teach them both! However, knowing how to play is the basic and you will have to show the person all the simple things to get started. Once he/she has mastered the gameplay and in-game features, you can then give them tips on how to win. All the best and have fun!