Here is an official explanation of the "I Quit" match from THQ.

• When your opponent is in a grounded state, press the B button (360 controls)/pin button to summon the referee to the grounded opponent. The referee will kneel down next to the grounded opponent and place a microphone in front of their face. It’s at this point that the I Quit mini-game is triggered. Stop the moving cursor within the designated target zone before the words "I Quit" fully materialize on screen to inform the referee of your desire to continue the match. If the opponent is unable to complete the mini-game in time, they'll automatically quit the match wherein they will be declared the loser. If a Superstar is in possession of a stored finisher icon they can use it to automatically win the mini-game and continue the match. However, doing so will result in the loss of that finisher icon. This option should only be used when you're at your most desperate.
• When an opponent is in the midst of performing the I Quit mini-game, the attacking Superstar can utilize an Intimidation taunt (by pressing one of the directional buttons on the d-pad) to increase the difficulty of the mini-game. Performing an Intimidation taunt will cause the mini-game meter to shake violently, which in turn makes it that much harder for the defender to complete the mini-game in time. Use of Intimidation results in a loss of momentum for the attacker so think twice before using it. If the attacker doesn't have a sufficient amount of momentum within their meter the Intimidation taunt can't be used.
• The I Quit mini-game can also be triggered by applying a Breaking Point submission hold on an opponent. Just like grounded situations, the referee will position themselves near the trapped defender wherein they'll position the microphone in front of their face. Complete the mini-game successfully to break out of the submission hold and continue the match. Failure to break out in time will result in a loss.