What game is this picture showing a character wearing a red bird costume from

The character is from the box art (and other promotional material, such as wallpapers) of Heroes of Might and Magic V, altough the picture has been heavily photoshopped.

This indie game is called "Crypt of the Necrodancer".

This game is quite new, being released in late April 2015, and has achieved very high ratings, 10/10 on Steam and 4.5/5 on Metacritic.

As you noted it's a rogue-like, (proceduraly-generated) dungeon crawler but incorporates elements from rhythm games. For instance the player cannot perform actions such as moving or attacking unless they perform the action in time with the beat of the music.