Fun fact: Paul Blofis indirectly saved the lives of everyone at Camp Half-Blood in the Battle of the Labyrinth
He didn’t move. I knew Grover was right. We didn’t have much time before Kampê returned. But I couldn’t just leave him here. Tyson would cry for weeks.
‘One game of rock, paper, scissors,’ I blurted out. ‘If I win, you come with us. If I lose, we’ll leave you in jail.’
Annabeth looked at me like I was crazy.
Briares’s face morphed to doubtful. ‘I always win rock, paper, scissors.’
‘Then let’s do it!’ I pounded my fist in my palm three times.
Briares did the same with all one hundred hands, which sounded like an army marching three steps forward. He came up with a whole avalanche of rocks, a classroom set of scissors and enough paper to make a fleet of aeroplanes.
‘I told you,’ he said sadly. ‘I always –’ His face morphed to confusion. ‘What is that you made?’
‘A gun,’ I told him, showing him my finger gun. It was a trick Paul Blofis had pulled on me, but I wasn’t going to tell him that. ‘A gun beats anything.’
‘That’s not fair.’
‘I didn’t say anything about fair. Kampê’s not going to be fair if we hang around. She’s going to blame you for ripping off the bars. Now come on!’
Briares sniffled. ‘Demigods are cheaters.’ But he slowly rose to his feet and followed us out of the cell.
Paul's trick is what Percy used to get Briares free, and then:
Then, behind me, something howled. A wall of darkness slammed into Kampê, sending the monster sideways. And Mrs O’Leary was standing over us, snarling and snapping at Kampê.
‘Good girl!’ said a familiar voice. Daedalus was fighting his way out of the Labyrinth, slashing down enemies left and right as he made his way towards us.
Next to him was someone else – a familiar giant, much taller than the Laistrygonians, with a hundred rippling arms, each holding a huge chunk of rock.
‘Briares!’ Tyson cried in wonder.
‘Hail, little brother!’ Briares bellowed. ‘Stand firm!’
And as Mrs O’Leary leaped out of the way, the Hundred-handed One launched a volley of boulders at Kampê. The rocks seemed to enlarge as they left Briares’s hands. There were so many, it looked like half the earth had learned to fly.
BOOOOOM!
Where Kampê had stood a moment before was a mountain of boulders, almost as tall as Zeus’s Fist. The only sign that the monster had ever existed were two green sword points sticking through the cracks.
From the way the battle was going, it's pretty clear that Kampê was the greatest threat on the side of the monsters, and she wasn't being stopped by anything Percy or anyone else could do. It's theoretically possible she could have been scared off by Grover's panic, but she's ancient, and Chiron's narration mentions armies being scared off, not someone like Kampê.
So, yeah, without Paul, Percy wouldn't have gotten Briares out, so Kampê would have been undefeated, and Camp Half-Blood would have been killed.
