I don't think it does apply to p2p loans. When I save $100 with a bank I retain my demand deposit - that $100 is still "there" for me. That is the multiplier effect (though that model has other flaws).

When I borrow $100 from p2p lending then loan it out to you through p2p lending I no longer have that $100 until you repay it to me, at which point you no longer have it. So we are simply passing $100 around without any multiplier effect.

edit - can't reply to you as the reply limit bottomed out - your response doesn't have enough info. You didn't address the demand deposit vs timed loan difference.

It applies to P2P loans in the macro sense. The proceeds from the p2p loan will be deposited in a bank somewhere, and then X% of that deposit can be lent out by the bank, and the cycle continues.

I owe you the $100 in the same way that the bank owes you the $100 you deposited. The only difference is that the bank is regulated and (FDIC) insured.