Please don't ban all screen time!! You'll end up antagonizing her and make things worse. Plus, we all know forbidding things makes them more exciting.
I looked up Dragonville and found this review: "A whopping 270 puzzles of various types and difficulties; up to 20 hours of gameplay; attractive graphics; many locations and characters; engaging heroine."
Maybe you need to be a little more open minded about her activities? Puzzle games can be very productive, and she may be the type of kid who 10 years ago would be doing crosswords and Sodoku - times change. Why don't you try playing with her one day? If she really loves games, there are tons of age-appropriate resources that she could use to learn to program and build games herself. She might enjoy some of the resources in this article:
http://www.apartmenttherapy.com/20-resources-for-teaching-kids-how-to-program-code-200374
Her interest in the news isn't completely alarming to me. Kids often have a hard time grasping the reality of situations that they aren't directly exposed to. Combine that with the violence, etc, in our TV shows and movies and I can see why she calls it "fun." I would embrace the fact that she finds the news entertaining, encourage her to learn more about the news stories that really grab her interest. For example, if she's really drawn to stories about conditions in other countries, encourage her to do more research into those countries, learn the history, culture, maybe even the language.
I think your best bet is to take the interests she is showing, and try to find ways to make those interests more interactive and productive for her. You can't change her, so embrace the things she likes and find ways to make them more fulfilling. It will probably help a lot for you to do things with her - play her games, watch and discuss the news, etc... it will probably help you feel better and help her think more critically about things.
In the end, while I understand your concerns, I think you can relax a little bit. The world is different now than when we were growing up, and she might be more productive/creative than you realize just because you don't fully understand what she's doing.
If you are worried that she may be depressed or struggling with some mental illness or developmental challenges, therapy is definitely an option, but I would be careful about how you present it. It's probably better for both of you to go together, and frame it as a family communication thing rather than a "something is wrong with you thing." Coming from someone who was forced into therapy because my mom didn't really get me or know what to do with me, she's not going to get much from therapy if it feels forced. Find a way to make it her decision, or give her some control over it, and it will be much more productive. Maybe tell her what you told us, "I'm feeling insecure about my own parenting skills, given that I didn't have great role models growing up. I want to connect with you and think it would be really helpful if we talked to a third party together. Would you be willing to come with me for an hour a week?"