How does Spaceteam work?

In particular, what aspect are you interested in? There is nothing special about mobile devices or ad hoc Wi-Fi networks (except for ad hoc networks, not all devices can communicate with each other, so some mesh networks can help, but unnecessarily complicate things for the usual case).

I'll answer a broader question first, because it's more interesting. In my experience, there are several basic considerations:

• Server / client or peer-to-peer? By this I mean whether there is a "master" deciding the true state of the world and communicating it to all clients. Avara is the only game I know, it is "peer-to-peer" in that sense (peer commands send commands to all other peers; this has proven to be a lot of bandwidth for modem users in 6 player games). I don't know of games that use more complex network topologies to communicate game state (e.g. only sending data to one client on each LAN).
• What are you doing with the delay? Avara is the only game I know of that is localized locally with "latency tolerance" to get a consistent state of the world, which was terrible if someone was on a modem (disabling compression helped a lot). There are various ways to "compensate for latency" (eg in Half-Life / CS), some of which can also work in peer-to-peer, peer-to-peer games.
• Time synchronization? For client-server games, you at least need to worry about changing the RTT. For peer-to-peer gaming, I think you also want to agree on timing that minimizes the effective maximum latency.
• What if customers disagree with the state of the world? Avara simply lets colleagues decide their own state of the world (and displays "reality fragmentation" if it detects a mismatch, which could be due to dropped packets or too low an "acceptable" wait).
• What if a player leaves? For a P2P game, you may need a consistent game state (for example, if a player was disconnected after sending commands to a subset of other peers). For client-server play, you may need to select a new master.

And now, after watching the Spaceteam trailer:

I have no idea how this works since I have not redesigned the protocol. However, it's pretty easy to do something that works well enough:

• Use some kind of P2P discovery to find players (like Bonjour, there should be a lot of documents and samples in there).
• Connect with peers. I did this with GameKit around iOS 3/4 (I'm not sure if it works over Wi-Fi).
• Choose a master. It can be as easy as the one who hits the "ready" last attempts to become a master. In some cases with edges, you may need a waiver.
• Let the master decide everything. Spaceteam is not latent sensitive; Wi-Fi latency is typically no more than a few milliseconds, and no one really will notice if one device is 100ms slower (as long as the UI is fast enough).