Syberia II, a 2004 adventure game, is the next Origin "On The House" game. It means, you can grab it for free as long as the offer is valid. And once you add it to your Origin library, you can keep it for life. Origin client is required to play the game.
You can grab it from here.
By the way, Syberia 3 is scheduled to launch next month. So most likely they're just trying to promote the upcoming game in the series. But anyway, it's free, so who cares?