is there any Sexism in video gaming?
This is a really broad question. I think you need to make the question more specific to make it worthwhile. Sexism is defined in different ways by different people (and different times).
Let's look at what I think is the interesting question. Video games are a form of popular art. They are created by people within a specific culture at a specific time and thus reflect that values and dreams and fears that relate to a certain point of time. In this way video games are no different than earlier art forms from popular music, to written stories and fold tales, to plays.
The ways that popular art deals with gender always reflects, in some sense, the ideas that are part of a culture at a specific point in time. In my opinion, this is a good thing. It is an artistic expression and it should be seen as such.
In the 21st century we now have this frantic search for "sexism" (which of course is a reflection of our culture at this specific point of time). Some of this is valid and interesting. Some of it is ridiculous (there is a musicologist named Susan McClary who claims that Beethoven's 9th symphony is sexist because the "throbbing" of the cellos represents rape).
As a father with a preteen daughter, I want this discussion to take place. I want us as a society to look at gender roles and to see where my daughter can be given the equal opportunity to live a full life. However, I want the discussion to be a real discussion where all of the sides are heard. It is very difficult to have this discussion (and in many cases, I feel it is the "feminist" side that is shutting down this discussion).
The interesting question with video games is the tension that exists. On one side is the need for free artistic expression in a popular art-form that reflects the feelings and fantasies of an audience that is traditionally young and male. On the other side are people who feel that any popular art should reflect the new sensibilities about gender and equality. In the middle is the problem of even defining what reasonable ideas about "gender and equality" are and who controls this definition.
One solution is for people to expose games that they feel are sexist and try to exert political and economic pressure to limit the production and marketing of these games.
This is happening, and it causes an understandable backlash since it allows a minority to put undue pressure based on their opinion of what should be permissible in games.
Whether this is a good idea is up for debate. One consequence of this trend is that it gives a large amount of power to censor content to a relatively small number of people... and these people get to set the rules over what is acceptable or not.
Unfortunately you don't hear this discussion.
The dialog has been stifled (and the misogynists can't be blamed for that).