Video game design

Tough one. Questions like this always bother me because I really, truly have no problem with supposedly sexist video games. I truly don't care that Lara Croft's body proportions are entirely designed for an ogling male audience, nor do I find it disturbing that female Mortal Kombat characters kill by blowing kisses. . .or something. Maybe this is a cause for concern, but I don't think so. This article reminds me greatly of a women's studies 101 course I took freshman year. What I took away from that class is that feminists need to lighten up. I've never been so thoroughly annoyed with women than I was after I took that class. Seeing as I am a woman, that says a lot. The feminist movement has value, but I get a little disgusted with just how much they read into things.
But let's assume that I do have to design a video without sexist messages. I guess my character would have to be very plain looking. Any emphasis on physical beauty or attractiveness would likely rile the feminists into saying that I'm creating a stereotypical media-constructed image of a woman. Fair enough. So we've got our plain female protagonist (with normal sized breasts and sensible clothing). What does she do? Well, seeing as it's a video game, I suppose she kills things. I can't really think of a popular game that DOESN'T involve killing things. I actually liked the bit in the article that talks about Lara Croft solving puzzles and riddles, etc. So I think that I would like to play up my protagonist's intellect and not just her skill with a machine gun. A nice balance of the two would be an appealing game, I think.
Honestly though, going back to the appearance, I think that's the real problem. Lara Croft was applauded because she was the one doing the ass-kicking, but feminists had problems because of her considerable. . . .err. . . .physical charms. So I think if you had a female character that was doing ass-kicking but had some practical armor rather than too-small shorts, there wouldn't be an issue.

Rituals and customs

I personally don't see what the problem is with using rituals and customs from another culture. The article chosen to illustrate the question is a poor example, in my opinion. This isn't so much a case of somebody disrespecting another culture so much as an example of gross medical malpractice. Frankly, who cares whether the doctor was treating the custom of the sweat lodge with the proper respect when the real issue is that he seems to have absolutely no idea how to conduct himself as a medical professional. By all means go to a sweat lodge if you're not a Native American. I'm sure it's quite physically and mentally cleansing. Just be sure that your host has, oh, SOME idea what he's doing.
In general, I think it's perfectly fine to participate in rituals from another culture. By that account, people shouldn't be able to learn Asian martial arts if they're not of Asian descent. Nor should non-Jewish people attend a seder, even if they are invited to one, as my family was a few years ago. It's stupid. Learning about other cultures is a great way to become more worldly, and participating in holidays and rituals is a good way to do that. Just be sure that, if it's an event/ritual of some religious or otherwise deep significance, that you behave in a respectful manner. And that you don' go to a sweat lodge hosted by a quack doctor.