Overall, this was just simply a bad draw for the Bulldog. Hogan, during the apex of his career, was basically this superhuman champion of right and all that shit. He was almost like a living cross between...I dunno...Superman and Captain America, he simply would not say I Quit. It's just how the character was made and designed. Even if there was a remote chance that the apex Hogan would say it, the Bulldog is certainly the wrong wrestler to try to make him say it. The guy has no submission experience at all and the guy just wasn't brutal. The Bulldog was primarily a big British powerhouse that could make Hogan feel pain, of course, but he didn't have the nature to beat someone so severely that they screamed I Quit.
The truth is, Hogan doesn't either. While he may know a little more about submission than the Bulldog, the apex Hogan wasn't vicious either. When it's all said and done, both are exhausted and the Bulldog just doesn't have the will to go on. He'd realize that he's fighting a fight that, under the circumstance, he just can't win. He'd have to somehow kill Hogan to win, he couldn't do it, so the Bulldog would just quit out of frustration if nothing else.