Girl gamers do not like the same games as men. Male gamers do not like the same games as other males. Tastes are wide and varried and everyone is different.
That said, there are some generalizations you can make between men and women and their interests. Men are more overtly hostile and violent. Our animal instincts incourage us to compete, and we enjoy having a direct conflict with a rival and bettering them is pleasing. Women also enjoy competition, but lacking in natural physical strength they naturally compete more in social manipulation, advancing their role in society through social interaction and bettering their rivals through popularity and opinion. Many women also stuggle with 3-D visualisation (this is a true, bizzar fact, as most women can not pass 3d testing to become air traffic controlers) but have superior organization and multi-tasking skills to men.
So, as a general rule, women will prefer less violence, more puzzle solving, higher social elements and 2D control versus men. This is not all women, and this is not all men, but there are some things that appeal to either sex more often than the other. As stated above, this is clear in movies, book, TV and games. There will be cross-over interests, but generally speaking it will always be mostly men playing Call of Duty, women will like 2D Mario more than 3D Mario, and while playing WOW a man will probably get off from slaying a dragon or winning a round of PvP in the arena, while his wife he met in Azeroth will enjoy the game more for the interaction she gets with him and other members of the clan, and collecting and completing a unique set of gear. Of course, my 73 year old mother loves popping someone with an automatic rifle in Blops2, but she's weird.
