Do those laws even apply to P2P apps without central servers?

Yes. Its defined without a technical requirement - just legal ones.

Each host will carry a legal responsibility for both what they push, and what they pull.

They do, but unlike what the OP claims, you do not need to age verify your site just because you added a social element. If the purpose is not to distribute pornography/other age restricted materials and you are able to moderate the site (ie: are not facebook scale), this is not required.

The law sucks but the misinformation around it is getting out of hand.

So if a site is completely p2p, it's illegal because it is unmoderatable?

No. If you are operating a p2p video chat site that is accessed by minors and you have no way for users to block or report content, then you are indeed going to face issues.

If a user is downloading a Linux image via bit torrent, or using WebRTC data channels to synchronise many clients using a p2p mechanism, what is the risk that needs age restricting?

This is what I meant, the OP is factually incorrect that just adding P2P technology to a service means it must age gate.

And if so, is BitTorrent also completely illegal now, even if there's no piracy? IPFS? I2P? Tor?