Peer-to-peer is the opposite to cloud infrastructure. There's no cloud service in where you have control over your own date, they always control it. With peer-to-peer and end-to-end encryption on the other hand you are in full control, even tho data is stored and processed on others computers too, and on your own.

If you where local only, then who's gonna control so that you don't cheat. Local only means that you're the cloud service if someone actually use and trust your computer.