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I just downloaded it and tried it. It is not P2P but cloud based. They said on the FAQ that those "Xims" (galleries) would expire after a while.

Doubt it's p2p, they probably just ship around a public url.

that would make sense but they keep more control when they use the cloud instead of a built-in web server

Actually, it wouldn't make that much sense. You couldn't guarantee that two phones were on the same network.

either way they have to be on the same network, cloud or no cloud, but anyways, most phones nowadays are connected to the Internet...

To use a local webserver, they would have to be on the same network (unlikely). To use the cloud based service, they would have to be on the internet (likely).

my local webserver is internet accessible (like many)