From developers Tequila Works, this side scrolling zombie game was released in 2012 for Xbox 360 and PC.
Although this game will be free for Xbox Live Gold subscribers as of April 16th, there is a free trial on the Xbox Live Marketplace for this game that has been available since it's release.
We follow our protagonist amidst a raging zombie apocalypse as he attempts to find his family after the outbreak, solving puzzles to get around and avoiding zombies as best he can. When zombies (also called "shadows") are unavoidable and you find yourself in a combat situation you are able to use melee weapons, and later on in the game guns but with limited ammo.
Below are trailers for this game from it's release in 2012.