It isn’t unforgiveness. The guy could have given him what he needed without him having to die from being tortured.
It’s like when an intruder busts into your home and you defend yourself by stopping the threat with your firearm. You didn’t intend for him to die, that’s an unfortunate outcome (for the criminal) of you stopping the threat.
The guy being tortured could have spared himself going through all that if he’d have just cooperated. Him dying wasn’t the goal, getting the info was. Him dying was an unintended consequence. Jack didn’t care if the guy survived or not, he needed the card one way or another. One way the guy could have lived without any torture at all, a whole other ways of varying pain but still alive, and then maybe several ways of him dying from different reasons. The guy chose to take his chances and hold out. The fictitious thug character lost the gamble and he died.
He was going to kill that dude, no question.