Second screen gaming is a type of gaming mechanic that has becoming more popular as our screens become cheaper and more prevelant. Think of something like the Wii U, where your controller is just a screen or has a screen in addition to hardware controls. It can display any sort of controller scheme you want. It can be themed to the game, or take advantage of a touchscreen which gives you greater dexterity than you could have with a DPAD for things like drawing games or swapping your inventory.
Using your phone as a second screen gives developers access to more sensors than just a touchscreen. A game could also take into account the accelerometer, gyroscope, voice, or anything else the phone may have.
Google is making it easier for developers to add second screen capabilities to their games. Being able to see your game on a larger screen makes the experience feel more cinematic, and it allows your friends to get involved as well instead of playing by yourself.
It’s easy to use the Chromecast as a screen while all the processing is done on your device. Android TV also supports casting, so you can use it as well to play some games that have newly added support for casting.
Some of the games that Google has highlighted include Angry Birds Friends and Monopoly Here & Now. In Angry Birds, you can see the world on the TV while your phone lets you fling birds. Google has been partnering with Hasbro. In addition to Monopoly, Risk, Yahtzee, Life, and Scrabble all have apps on the Google Play Store that support casting. They take advantage of the second screen, like showing your cards on your phone while the playboard is displayed on the TV.
The full list of games is available here, with some of the newly supported games at the top.