Disclaimer: I am not a parent, yet, and I am not a girl. On the outside at least.
They will play games. The next issue will be what the games are made of.
I used to play _The Oregon Trail_ in school. I learned to laugh at the misfortunes of others and that having 100 boxes of ammo alone can get you across America. I did not bother to look up what "dysentery" means until college.
There are beautiful puzzle games like Eufloria and Echochrome which are visually stimulating and [probably] fun while being deep in the safe side for youth. The latter you would need to watch a demo to understand how thoughtful and potentially educational it can be. There are also some touch games like Crayon Physics which are even more interactive.
Why not more popular games like Angry Birds and such? Well I like to classify games based on different mindsets, player capture/retention schemes, time investment and reward levels. Based on my observations, there are much better selections out there.
Games like Angry Birds and super popular games become popular because of "overwhelming rewards" which are instant and audio-visually gratifying. Explosions and points are on a very superficial level. The mindset is simple and whatever physics present is overwhelmed by glitter.
This paradigm leads to what I can only describe as an addiction to a very basic stimulation. It is present in all genres of games so It may be hard to pinpoint what I am getting at.
The next level of game balances visuals with actual complexity- meaning less chance of trial and error reward freebies yet not as fast paced and stressful as hardcore puzzles.
The extreme end of this would be Tetris and Pac-Man which is "trouble-avoidance" rather than "reward accumulation" type.
The three games I recommend are of a walking pace, enough to pique interest and momentum though increasing complexity yet will not evolve into a "trouble avoidance" model or decline into a thoughtless plateau of "reward hoarding."
I will not suggest anything multiplayer over the internet for obvious reasons. Competition and cooperation are valuable to growing up, but in my opinion should not come from interacting with unknown parties over a medium you have effectively no control of.
There are youth oriented MMO "games" like Disney's Club Penguin which entails buying stuffed toys or tokens and other trinkets for virtual redemption. This strikes me as perversely over-consumerist and potentially hazardous to a child's self esteem. Any game based on real currency investment is asking for trouble. If you may think buying designer clothing for a 10-year-old may be over the top then you know ridiculous it is for a child to buy virtual status with (probably your) hard earned real money.
Imagine all the issues of lunch period social dynamics at school, except with amplified temerity in all parties granted by anonymity and physical disconnect. Would a parent really want this for their children's leisure time at home?
Choosing a game fit for your child is not an easy task unless you have experience with a wide gamut of games, and wide it is. From "free" games that are nothing less than exploitative (in the sense that it exploits the base urges of the mind, rather than challenge the mind) to blockbuster games down to classic puzzles, you have thousands of titles to choose from.
The most depressing thing I've learned so far is that games that fit this age group are mostly empty in substance, banking on popularity, naiveté and social media.
With regards to the investment, there will be different kinds ranging from freeform where the more they play the more rewards or complexity they gain. Fixed or semi-fixed timeframe games are ones that depend on real-life timescales and limitations. Many social media type games only allow a certain amount of investment per day or some other schema. Avoid these. In fact, gaming should be education(hopefully) during leisure time, not virtual feudalism during real-life time.
Irregardless of age, the issue of investment on low tier exploitative games often leak into the players social life, hijacking friends in order to grow the game's popularity. Viral marketing, very literally. No you will probably not let your children play Farmville on Facebook or its numerous clones but don't let it's popularity mask from you from the low-class system I described above that it thrives on. Much of today's iPad Top lists are filled with these schemes. The iPad is a wonderful tool for young generation of gaming but it will be even harder to find quality content on this platform. Ironically the three games I suggest above are found on Playstation Network and iOS and the such. This should show you that quality does exist, so learn to pick out the signal from the sea of noise.
I'm not telling you to make your daughters play Bridge, but if you want to be well informed then you will actually have to skip the "Top Grossing" lists and do your homework because video games are a serious business and may have lasting effects on your child's development because it definitely had on mine.