Personally, my parents taught me that women should be respected. I tend to be a bit nicer to my triplet sister than my brother. This doesn't really affect my door opening, though, since I tend to hold it for most people. So what if I tend to be a bit nicer to the opposite gender? It's not like it hurts anyone, and when it comes down to it, how I treat people mostly depends on how they treat me.
On the subject of videogames, They way overdo it with the sexualization of female characters. It's annoying, to say the least. The thing is, I guess this is due to the demographic of gamers who they are aiming for.
My sister tends to play more RPG-ish games like the Tales series or Disgaea; she does really like the Mega Man Zero series and Castlevania, and she plays TF2 with her friends at school also. She doesn't like overly gory or scary games like Left 4 Dead or Dead Space, and she tends to not play FPS or fighting games. She might be an exception, though.
Edit: Well, there are always exceptions. :b