Alright, since this question seems like it was answered in the comments, let's turn that into an actual answer shall we?
Photon Unity 3D Networking (PUN) works by connecting people to each other instead of to a server for gameplay implementation. So, in short, it works with P2P networking. The most popular example I can think of is Call of Duty Modern Warfare series that uses this sort of (P2P) networking.
The biggest issue with this implementation is that the server is actually a player and should they cheat, it would be really hard to catch them (a reporting system would be necessary but since they have the server on their machine now, chances are, they could mask their username to something else).
The solution that Photon Engine offers is the Photon Server although this sort of P2P method could be used with other kinds of servers but it would take a bigger effort than using their own server implementation. Time versus money kind of deal.
Quote from the asker because these comments are also relevant to the answer itself:
You have to install Photon and run the server with it using the
binaries. I guess these binaries get uploaded and started on the
Photon cloud. They even seem to have a Unity api for this but the link
to the documentation does not work.
Well, it does seem like PUN is not useful for a competitive game. It's
an amazing framework to create something like Wordfeud or Hangman to
play with your FB friends. But nothing that is even really
competitive. I got Photon server working currently and it seems to
have potential. But the price is kinda high if you compare it to
something like KryoNet or Lidgren and pay to host it. I also dislike
the development, on each change I need to build the server, put the
binaries in a folder, restart photon and start the server again.
Normally you would just run the server from your IDE.