I'm guessing the app has a small built-in webserver - or perhaps relays through a 3rd party webserver - and the others join up in their browser using some kind of websocket like transport? Wonder if they direct the others to the app user's phone's internal wifi IP?

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)

Not really, you just get a URL to send to your friends

And who doesn't have a browser? I can't think of any better solution than this.

High quality photos means a big data hit, for those that don't have unlimited data. It also puts your photos in the cloud, which may not be desirable.

the web is available everywhere unlike the apps... (the app could even be web based)