That Gun is a uniquely named 5.56 caliber pistol.
That Gun originally belonged to Domino Mask who presumably owned it before the war and kept it well maintained over the last two centuries. Domino left That Gun behind with his luggage when he entered the Casino Royale. Dead-Shot acquired the pistol during his escape when he fled the the resort. Dead-Shot now carries the pistol as one of his primary sidearms.
The 5.56 pistol model pistol is officially known as the IF-69. The pistol was built by Ironshod Firearms during the war and is designed to chamber and fire rifle rounds as opposed to bullets. That gun has notable recoil and its ammunition is loaded into cylinder like a revolver.
- That Gun is a unique 5.56 pistol from Fallout: New Vegas