Hacking is a waaaaaay difficult thing to do in this day and age and it mostly occurs on systems with a lot of 3rd party services opened towards the web (like the servers that web sites are hosted on) and home computers of morons who can't see enough lolcats.
A game server is a an inhouse developed service, web opened towards player authentication only (which authentication lets you only do stuff to the account, not to the server). So a hacked game server happens when the game company employs idiots as game developers or as internal IT security (opening a phishing email on an accounting computer shouldn't allow pivoting to the main game servers).
Hoping this was clear enough to calm your fears ...