From a couple months ago, their estimated revenues for 2011 are $1.8 billion [1]. This is a completely different beast to linked in. I'm very interested in seeing how it goes.
[1] http://blogs.forbes.com/afontevecchia/2011/03/02/zynga-revea...
[1] http://blogs.forbes.com/afontevecchia/2011/03/02/zynga-revea...
Zynga is mostly a modern spammer, as far as I can tell, and the spam business is a constant arms race. They can't win it forever, unless facebook remains mostly complicit in the process (which would hurt facebook in the long run, even if it is profitable for them in the short run).
So, I'd believe that Zynga is making money, even a lot of money, but I have a hard time believing they can sustain that level of profitability as people's tolerance for facebook spam declines. And, I have a really hard time believing those specific numbers. I guess there really is a lot of money in stupid.