To really understand this, I think you have to take a step out of games and look at the common demographic that is being represented in video games: white, male adolescents. Anybody who plays XBLA or any other online game can attest that these are at least the most vocal, if not the most common demographic, and it's generally these people who are throwing around racial and sexual epithets.
This same demographic is often seen saying similar things outside of games and Internet forums. Listen in to a group of young men speaking and you're likely to hear "gay" and "fag" being used not only as insults, but as substitutes for words like "lame" and "asshole". The fact that these words have sexual connotations may not even be a concern to these individuals -- instead, it's often just a generic term with the same power and amibiguity as "shit" or "fuck".
On the other hand, the sexual meanings of these words may be no mistake either. As a white male myself, and once an adolescent, I can attest to masculinity being a major part of growing up. No different than a pack of dogs, every male wishes to be the alpha male and any who isn't looks up to that individual. Being weak or otherwise different from the alpha male is seen as inferior and therefore shunned from the social group.
Why the hatred towards homosexuals then? It's not that homosexuals are somehow weak, but to a male population whose mind is preoccuppied with the opposite sex, a man who is not enamored by women is seen as different, strange, perhaps even damaged. I was treated no differently than a homosexual -- often accussed of being gay -- not because I had an interest in men, but because I hadn't yet developed an interest in women. As with any group trying to establish an identity, failing to identify with that groups' principles excludes you from the group.
So why the angst towards women? Myself, I find it hard to understand, but I was also brought up in a family that lived and preached male/female equality; though I was still exposed to such prejudices from outside. I think part of the problem is similar to above: women are not men and that makes them inferior in mens' eyes. This is no different of an argument than that a cat doesn't roll over, play fetch, and otherwise make a very good dog; a woman isn't suppossed to be a man, so it's a non sequiter to argue that she doesn't make a very good man.
The other problem may be one of mens' interest in women and how that's marketed. There's no denying that men look at women and think about having sex with them; likewise, women will do the same with men (so I'm told by many a woman). However, there seems to be an attitude in marketing (video games, TV shows, advertisements, and music videos are just some examples) that women are sexual objects for a man's gratification. It's hard to explain why female characters in video games are unrealistically shaped (no woman with 44"/DD breasts has a 28" waist and weighs 110 lbs. without serious health problems) and dressed in a manner rarely suitable for the beach let alone sword-fighting, without admitting that games are specifically being designed to sell based on sex. And judging by the success of games like Grand Theft Auto IV, it's hard to deny that males are enjoying the sex that's being sold to them.
So are epithets against women, homosexuals, and other races a problem of anonymity, or do they already exist? I would argue that, despite society taking a stance of "tolerance" in public, the people themselves still hold all of the same prejudices personally and when taking into an anonymous or semi-private group setting, the old tennets come out in spades. The fact that we see certain biases so prevelantly in video games is not because gamers hold those biases, but because the major demographic of gamers holds those biases independently of being gamers -- the gamers are instead a smaller section of a much larger demographic who all tend to have those same biases.
To the women, homosexuals, and every dehumanized race out there, my apologies for my countrymen. It's a shame that so many people in my demographic feel the need to certify their own superiority by denying the worth of everyone around them. Rest assured that some of us still understand that differences aren't necessarily a case of better vs. worse and that, despite having some of these impulses within us, we have the better judgement to look past them and see each other as human beings and not as outsiders or sex toys.