The ESA numbers might be true in the most liberal sense of the word, but everyone has to remember that they are provided by a lobbying body of the industry (which also stood up for things like SOPA in the past in the name of said industry, even though separate publishers when pressed on it would either say a different thing or not answer at all) that is supposed to make the entire Gaming Industry look good and presented in a misleading way without providing any further details.

The same study for instance also says:
"89% of the time parents are present when games are purchased or rented"
"80% of the time children receive their parents' permission before purchasing or renting a game"
"93% of parents pay attention to the content of the games their children play"
If you believe this, I have a bridge to sell you.

http://www.gamasutra.com/blogs/WandaMeloni/20100330/87019/The_Next_Frontier__Female_Gaming_Demographics.php
http://www.datagenetics.com/blog/december12010/index.html
http://psychology.wichita.edu/surl/usabilitynews/141/videogames.asp
http://massively.joystiq.com/2013/06/03/96-percent-of-eve-online-players-are-male/
http://www.goodluckhavefun.net/league-of-legends-infographic/
http://www.casualnews.com/the-demographics-of-social-games-surprise-or-not/
http://readwrite.com/2013/04/11/why-mobile-game-developers-are-on-the-cusp-of-a-golden-age

If you look through these you will notice that the split between games differs a lot, especially based on type of game and genre.
"Core" games like GTA, Call of Duty, Battlefield and similar that sell in the millions at retail and set up new records every year, even outdoing the movie industry are mostly male-led.
CoD is 92% male, League of Legends is over 90% male, GTA IV is 85% male, EVE Online is even 96% male.
These games largely cater to their market, which are males usually between 12-30 years old.

(Notice how for instance how EVE Online or League of Legends had female character options and female champions from the get-go and this didn't particularly help them garnering more of those demographics.)

On the other hand games like Bejeweled, Treasure Isle, Country Story, Happy Pets or YoVille with ~80% or Farmville and Restaurant City with ~70% female players are female-led.
Most big publishers have female-led franchises that cater specifically to that demographic, EA for instance has The Sims, their Harry Potter games series, Bejeweled, The Sims Social, Pet Society and similar.
http://gigaom.com/2010/02/17/average-social-gamer-is-a-43-year-old-woman/

The Sims and The Sims 2 are both in the Top 3 of the best-selling PC games of all times with The Sims 3 not far behind and rather far up on the list best-selling video games of all times. They cater largely to women.
http://www.gamespot.com/news/ea-women-too-big-an-audience-to-ignore-6169357

Contrary to popular belief games like Dragon Age or Mass Effect aren't played by that many women though, no matter how hard they might try to appeal to said market and they still have over 80% male demographics: http://www.eurogamer.net/articles/2011-07-20-bioware-18-percent-play-mass-effect-as-femshep
http://cdn2.gamefront.com/wp-content/uploads/2013/03/mass-effect-3-infographic.jpg

UbiSoft has games like Just Dance, Your Shape, Petz, their Imagine and My Coach series (those are rather large, further games that get utterly ignored): http://www.commonsensemedia.org/game-lists/imagine-games-girls
Exploratory Adventure games like Myst/Uru have also been rather successful with that demographic in the past and there are still a healthy dose of those around: http://www.minotdailynews.com/page/blogs.detail/display/1000/Women-play-as-many-video-games-as-men.html
http://www.sophiageorge.com/uploads/7/4/7/6/7476345/engaging_women_in_games_using_emotional_stimuli.pdf

Adventure games in general have a wider female audience, see for instance The Blackwell Series, The Longest Journey/Dreamfall, Emerald City Confidential, Secret Files Series, Haunted, Gray Matter, Syberia Series, Nancy Drew Series, Still Life Series, Broken Sword Series, Edna & Harvey Series, A Vamypre Story, Winter Voices, To The Moon etc.
As well as the largest number of Hidden Object games: http://www.youtube.com/watch?v=0Npu8xQDxS4

Don't get caught in the trap of saying that game publishers "aren't trying" to make money or wouldn't go for a specific market if there was money in it, because they do regularly and a lot of these products prove that. They just find out that in financial terms gender specific games that many feminists might theoretically not agree with sell very well to girls/women, while games with a high amount of action and violence and "core" AAA games generally don't.

This isn't "sexism". It is simple business and common fucking sense. The genders are generally speaking different enough to want different things. Catering to your main market instead of retooling your game to appeal to an entirely different demographic or turning the games into a homogenized mess that the main market would never buy is what more publishers and game developers should be doing, not less. (Notice how big games like GTA, Call of Duty, Hitman and similar usually get the brunt of the complaints of having to change.)

Other games that are generally overlooked in these talking points are lower profile Indie games like Contrast, 99 Spirits, Lilly Looking Through, Memoria, Game Dev Tycoon, Assault Android Cactus, SpeedRunners, Hate Plus etc. that never get brought up.
Not to talk about games only showing up on even lesser known game distribution methods like Desura, iOS/Android or on Casual game portals.

There even exists a subset of Japanese games that basically boil down to being romance games for a young female audience:
http://www.englishotomegames.net/list

Very few if any of these seem to ever show up on thorough lists regarding female protagonists in games like the ones on Mobygames or Giantbomb, since they are utterly ignored: http://www.mobygames.com/game-group/protagonist-female
http://www.giantbomb.com/female-protagonists/3015-2287/games/

Yet a small bit of the industry that largely coincides with the console AAA market and makes up what is possibly 5-10% of the entire Steam games released nowadays at the most seem to always be the only thing that get looked at in these cases.

It's not even that the "AAA" industry didn't try, there are also a lot of examples of AAA-ish games out there with female protagonists: Oni, Mirror's Edge, Beyond Good & Evil ( http://www.escapistmagazine.com/news/view/129370-Ubisoft-Considers-Beyond-Good-Evil-a-Mistake ), WET, Velvet Assassin, Heavenly Sword, No One Lives Forever I+II, Remember Me (a very recent commercial failure), Zanzarah, Venetica, American McGee's Alice, The Wheel of Time, Drakan, Bayonetta, Hydrophobia etc.

Aside from Tomb Raider (which sold extremely well on its sex-appeal when it was a fresh franchise), Portal (with a silent protagonist) and Metroid (which is basically a robot game and at the end it is revealed that the pilot is actually female) none of these games sold "AAA" numbers and none of them could develop into a franchise, which seems awfully important for most big publishers nowadays.

Arguing that "core" games with a 90%+ male market buying them need to change because a large amount of women are playing what amounts to a majority of Casual, Facebook and Mobile games is stupid.
Arguing that Social/Casual games need to change and offer more Space Marine and Modern Warfare variety because a large amount of men are playing "core" games would be equally stupid.

And before more people start arguing demographics, marketing and prejudices, one of the articles made a very good point, which is that you can even easily conclude to a product by just looking at its demographics data alone (which you can as easily apply to games):
http://i.imgur.com/Q0e4CsR.png

What the SJW are often essentially asking is not only to change games, but for companies to forego verifiable for-profit motives and existing audiences while trying to harness and force them to help "change society" and try to reeducate their audiences to be in line with their idealized model of the world by somehow magically making people like things they normally wouldn't.