Is Duolingo playing games with us?
If you mean the usage of gaming aspects, yes duolingo is using them heavily and this is called "Gamification". The word refers to usage of game dynamics and mechanics in a non game context to engage users. Duolingo uses leaderboards, points, levels, sharing, achievements, unlocks, badges (mastering courses), progress bars. I am currently writing an article on this actually. For more info you can check this link: http://en.wikipedia.org/wiki/Gamification