In the Hobbit movies, Thorin is stabbed by Azog two times: First in the foot and then the chest. The second stab was potentially fatal. Yet how did Thorin survive such a fatal stab, let alone have the strength to kill Azog ?
He probably missed Thorin's heart and hit around his stomach. Here's the picture from this video at 3:47
In a human (and probably an orc), that's about where the heart would be, and so it would be reasonable to assume that this is immediately fatal. But Thorin is a dwarf, not a human. Assuming dwarves are simply more compact humans, that would probably move his heart up a bit.
Since Thorin is still alive but nearing death when Bilbo finds him, this would fit well with the assumption that this is a stomach wound. Those wounds lead to lots of internal bleeding and take a while to kill you.