So as with any useful tool, someone who gets comfortable enough using a computer is going to start to play games. Now, if you bought your computer yourself and put it in your own home, you have every right to do so. However, your computer at work is NOT a toy. You are probably not supposed to be playing games on it.
Now, Minesweeper or solitaire, not a huge deal really. The only beef I could see an employer having with that is that your productivity may not be what it should be. You may be distracted. When I get pissy is when I start having to rush over and fix virus and malware issues because you clicked a link in Facebook to play Farmville, and now all of a sudden you're getting popups for anti-virus programs that are really viruses...
Ok. I realize we're all human, and if your work is done, you probably deserve some screwing around time. It's really not that big a deal. But honest to god, it is the most difficult thing to be dealing with something that a user caused, WHILE getting grief about their computer being unavailable. I know you didn't intend to install the malware, but you did. I can't go back in time and prevent it, I can only fix it.
It's like trying to drive through a six foot deep puddle, and then complaining that you have been without your car for the last two days while the mechanic is replacing your engine. I'm sure he'd realize that you thought you could make it, but you didn't. Now there's work to be done.
Facebook games are the worst. Most are legitimate, but the ads that come on the page aren't always.
If you can't simply use your work computer for work, and you're hell bent on playing games on facebook I recommend using a browser other than Internet Explorer. Use FireFox, and install Adblocker plus. This will lower your risk of infecting yourself.