You just had to use the analog stick. Push it in any direction once you had a full Revenge meter, and it did the finisher.
Some finishers, you had to grapple, some you had to strong grapple, some you did when they were on the ground (like the Sharpshooter, etc.), some you did from the top rope.
I'm not going to clown on you for not realizing that, though. It was weird that the N64 controller had an analog stick, but you used the D-pad for moving and the stick only for doing finishers. You would think it was the reverse.