It's almost like a Tarantino scene, in that it's five solid minutes of two guys talking quietly, followed by one of them killing the other in the most laughable way possible.
It's also much darker than what ended up in the film: First of all, Simon actually gets away with the gold he stole, while McClane is fired from the NYPD and his pension is taken away. Like in the movie, McClane eventually tracks down Simon thanks to a bottle of aspirin Simon had given him earlier; unlike the movie, McClane also brings the aforementioned rocket launcher and insists they play a game of Russian roulette with it. Simon wins, and his prize is a rocket through the chest.
20th Century Fox
"All right, let's try best out of three."
So, you see, that's the "vengeance" from the title -- it's not Simon going after McClane for killing his brother two movies ago (he didn't give a shit about that), it's McClane taking his revenge on Simon for ruining his life. Also, this scene takes place on Christmas, McClane's preferred date for killing bad guys, according to the previous installments.
However, according to the DVD commentary from screenwriter Jonathan Hensleigh, the studio felt that this ended the character of John McClane on a bit of a bad note. McClane has killed a lot of dudes over the years, but it's always in self-defense or to prevent them from getting away. In this case, Simon already got away. This would be the first time McClane went out of his way to coldly murder someone, and the studio felt they couldn't allow it.
Because, you know, that would have ruined the franchise.
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Yes, rocket launching vigilante McClane. Nothing could be worse.