Amazon Prime members who play games or have loved ones who love to play games have received some good news from Amazon. Amazon is offering 20 percent off discounts to new games. This means that this deal is available for games during pre-order and for two weeks after it’s release.
— Amazon Video Games (@amazongames) January 12, 2016
It is automatically applied at checkout. It is only valid for games that are sold and shipped by Amazon. This is for physical copies only, not digital and if you buy a game from a different seller then the offer will not apply. If you have already pre-ordered a game in some recent time then the offer should automatically be extended to that.
No word yet if this extends out of the US store and into other regions.