Elminage Gothic has the option to enter a custom alignment. Wouldn't have been that much of a stretch for them to have offered the option to enter a custom gender, especially since "?" is already an option. It feels like a missed opportunity to me.

Male vs. female is sex - it is the biological distinctions. Penis vs. vagina.

Gender is man vs woman, masculine vs. feminine, etc. - the social distinctions. Like skirt vs. pants, long hair vs. short hair, pink vs. blue, things like that. Gender is more like a continuum rather than two discrete categories since the definition of the genders varies over time and from place to place. Gender depends on the culture.

For example, before the Holocaust, pink was regarded as the masculine colour, blue was the feminine colour. But after the Holocaust it became reversed.

Gender is really just about fashion trends really. What is considered feminine now might become masculation. Women back in the day weren't supposed to wear pants. That was taboo. That was transgenderism back in the day. But now women wearing pants is normal. It doesn't really mean anything.

Personally I would like to see options for both sex and gender in games. But in terms of gender, it is probably enough to allow the player to choose hair style, clothing, and all that. For example, I find it extremely easy to make feminine male characters or masucline female character in many games like PSO and Dragon Age. That is probably more than enough really.

I really wish there was less care in some corners of the internet about games giving people their sexual preference and more about the game-play and story-line.
Quite frankly if you want a game with a completely fluid sexuality and fun game-play try Puddle
http://www.gog.com/game/puddle

Pyrofox?

If you going to choose in game, may you choose a masculine child.

A tad more than that, as body attitudes (the way you walk, sit, run, move, the intonations of your voice) and your activities are gendered as well. Societies define "a real man" and "a real woman" with lots of other (more or less 'strong') factors than fashion. They educate them to "act manly" or to "act womanly" in reference to a local cultural definition of manhood and womanhood, and this goes way beyond what to wear.

And some societies label some (biological) "men" as "women" (socially), and the other way round. A gender can be attributed, if there is a consensus around calling a (biological) man "she" and to set expectations accordingly to that. For instance, some amazonian natives giving some male homosexuals a "woman" role in society. Or a status that is neither male nor female (a third gender).

Anyway, not sure how this distinction would translate in games...

Easy, you just don't limit game features by gender, is all. So if the setting has male swordsmen who wear kilts and female archers who wear pants, the player character can have any avatar, any form of address, wear either article of clothing and master both skills as skill points allow, without penalties.

Great, but I can't even claim credit for it. I think Futurama already did it. They were way ahead of their time to allow so much air time for MCTLPBTAs.

browser game Fallen London/Echo Bazaar let's you choose "Unspecified". not sure about Sunless Sea.

some of the races in MOO might be asexual. likewise the mages in MOM, and the heroes in HOMM 3.

Actually, it is more complex than that.

There is chromosomal sex (whether the person is XX, XY or something else). There is genital sex, which doesn't always coincide with chromosomal sex; for example, having XY chromosomes doesn't mean one can't get pregnant and give birth [1]. And of course, there are secondary sex characteristics that aren't guaranteed to match either.

Then there is gender identity; that is, whether one perceives oneself to be male, female or non-binary. Again, this doesn't necessarily correspond to either of what I mentioned.

Of course, all this is independent of romantic and sexual orientation, as well as gender expression. I think a link to the genderbread person might be appropriate [2].

[1] http://humrep.oxfordjournals.org/content/12/7/1434.full.pdf
[2] http://itspronouncedmetrosexual.com/2015/03/the-genderbread-person-v3/

Yeah. I haven't played RPGs for ages, so I had typed my post under the impression that this was much more common than it is. My last contact with a customizable-character game was a saint row video, which seemed very naturally permissive on that. But thinking about it, this isn't the norm at all.

Eek, yeah. I had hesitated to go into "intersex" territory in my post, actually, with the question of doctors sometimes chirurgically deciding and imposing a gender to the person (blurrying the line between societal and organic). But that's quite the epistemic rabbit hole...

Of course, the results of imposing the wrong gender are not pretty. See:
https://en.wikipedia.org/wiki/David_Reimer