Is it possible to connect to a game server via a socket and return the number of players online via a !ponline command?

It is, but you need to know all of the protocols required by the gaming server to do so. Also, some gaming servers do not allow such third party connections and if you were caught, your account may get deleted or you may be banned from the server(s) or some other consequence. So keep that in mind if you decide to try.

I am the owner of the server.

How do I find out what protocols?