There is one aspect of Gygax's words that I haven't seen mentioned that occurred to me:
We know the parts of OD&D books that are considered problematic, and his forum posts defending biological determinism. From these we know that Gygax realized fairly early on that D&D, in his experience, did not appeal to female gamers as much as it did to men.
So that puts a little more context to his1975 comments in EUROPA magazine: he knew that D&D did not appeal to women. He received feedback telling him what he could do to make it more appealing to women (more emphasis on the female role, more non-gendered names, etc...). So how did he react?
His defenders say he responded with sarcasm. Is this really a defense though? Women reached out to him to tell him how he could make D&D more appealing to them and he responds with sarcasm. A sarcastic response is not a joke - it is a way to tell your audience that you do not consider the triggering statement to be worthy of a serious answer - and this is directed towards people who are interested in the game.
( for the record, I view the first part of his comments to be sarcastic, but everything from "Damn right, I'm a sexist" is in deadly earnest. I can't envision using "damn right" for emphasis in a sarcastic manner - it screams real anger to me)
And then, years later, he talks about biological determinism, in which he comes right out to say, effectively, that women do not like to play games, except for the games they do like to play because those aren't really games. And he used an example of Lionel making pastel colored trains to appeal to girls as evidence that coding toys to girls doesn't work.
Can you really read Gygax's forum posts without seeing them as an " It's not me, it's you" response?
Gygax was told early on what he could do to make D&D more appealing to women in a way far more significant than coloring things pastel. Rather than using this as an opportunity to learn from his customers, he sarcasticly mocked their concerns and justified it by blaming everyone else, rather than consider that his game could be improved.
TSR era gamers were < 10% female. Currently, the numbers are around 40%. Maybe if Gygax had taken the criticisms seriously and made an effort to appeal to female gamers back in 1e AD&D and B/X, TSR would not have been in the dire financial straits of 1984-85 that led to the management shakeup.
But in 2005, he was still blaming women for having the wrong type of brain to enjoy D&D.