Mental illness/child neglect/child abuse are all tragic things that exist independently of media.
If the title of this article were "Study shows link between social media and depression" it would be a different story.
Right now the gizmodo article is titled something outrageous just to illicit hits to their site.
Disclaimer: I've never played Farmville. I assume it's non-violent gameplay.
The only thing violent about farmville is how zynga relentlessly pursues your email list and real life dollars in exchange for worthless worthless digital items for your farm.
Zynga does do a bit of charity awareness and fundraisers in the game (the Haiti Earthquake relief fund, for example) but the best way to get blocked from everyone's news feed is to post a bunch of farmville stuff on your profile.