In addition to the fighting part, each move cost some amount of energy. Energy was accrued by successfully attacking the opponent. At the start of every standoff, a random number of energy (spirit, I guess) was shown in the center of the screen. If you won the standoff, you'd get that energy to use for attacks. This meant you couldn't just spam the strongest special over and over because you wouldn't have enough energy to execute it.
The intricacies are worth looking into if you're interested, but I thought this was a perfect mechanic for the wrestling game. Each grapple can only be executed if a player has enough energy, or in this case "momentum". Momentum is gained by being the one to execute the special move (the skill based timing game for when the lockup animation happens). The amount of momentum gained is based on what is currently in the pot, which is randomly selected like in the Yu Yu Hakusho example.
You lock in your grapple before the lockup/grapple attempt happens. You also expend your momentum regardless of being the one to successfully execute. It also allows for the ups and downs since gaining a large lead in the beginning won't necessarily win you the game if the opponent has better timing than you and is able to secure the momentum for a big move.