Is the game sexist?
The game itself isn't this or that. But it can be recieved in a cultural context in which it is supporting sexism, yes. There is a difference. Art doesn't have any obligation to ethics. But the way art occurs in a society is a reflection of the ethics of artists and consumers alike. This means that Duke Nukem isn't *anything* as far as I'm concerned. But that Duke Nukem exists and is celebrated tells us that there is a lot of sexism in the developing and game playing community, absolutely.
Demonizing Duke Nukem for being a honest reflection of how people feel isn't going to do anything. It's a product you can buy or not buy, enjoy or not enjoy. But a broader discussion about gender roles in the video game industry and in the video game playing community absolutely is affected by something as high profile as Duke Nukem 'tapping asses'.
How about the characters?
A character isn't sexist. What a character says about creator and adopter/consumer though, is very much open for discussion.
What about the game development community?
Absolutely ridden with sexism and chauvinism, and not even of the ideological kind. The kind perpetuated out of sheer ignorance and perception bias.
Will any of this effect it's reception (in the gaming communities) or sales?
I don't think so, significantly, no. Duke Nukem already preached to a very specific choir, I think.
Does this mean throwing the damsel around in Spelunky makes me sexist?
No it doesn't. Please consider for a moment how it'd feel to not be part of the most privileged social group in the world (first world, white, young adult, middle class, straight, male). Please consider how it feels to be on the 'out' while people constantly belittle your problems with being in the out. Being a woman is hard. Spelunky has nothing to do with it. What people sweep under the rug and call non-priviledged Others hysterical over sweating has everything to do with it.
If you consider sexism and chauvinism a bad thing, something you'd like to see less of in the world, you can start by being more sensitive to the plight of individuals who aren't in your priviledged position. Just to consider them. It took me a long while to get to doing that as well.