As those who know me will know knowingly with their knowledge of me, I'm a gamer... of sorts. Well, I like my games. A lot. I go through phases of heavy gaming and little-to-no gaming, and currently I'm tending towards the former. I've mostly been playing strategy and role-playing games lately, and the way they can deal with gender may be surprising. I've got a number of strategy games, largely from Europe. Anno 1404 and its expansion Venice, Anno 2070 (the latest in the series), The Settlers VI, The Settlers VII and Patrician IV. To contrast this I've been playing The Elder Scrolls V: Skyrim. I'll describe how they represent gender, and then continue my thoughts.
Anno 1404, Anno 1404: Venice & Anno 2070
The user is allowed to pick a user picture from a variety that is provided, whilst others can be unlocked through gameplay. Largely they're male, but there are some females of varying ages. This has no bearing on how the game reacts to the player, as the user pictures do not define gender.
The Settlers VI
The player is designated as 'male' via cutscenes in the main campaign, but with no elaboration. There is no physical manifestation of the player, and one must assume that the player's gender would have no bearing on the story whatsoever. The player is, however, allowed to choose from (at the point I'm at, which is Mission 8 or 9) one of six characters - four male, two female - as their knight. This knight is a special character with unique abilities and is essential for gameplay. The character chosen has no bearing on how the game reacts to the player.
The Settlers VII
Now, this is a good one. The main campaign that comes with the game has a single playable character - Princess Zoé. There is no room to choose. The smaller campaigns, including those in the additional content packs, tend to have fixed characters too. The player is cast as Princess Zoé (or, with a little outside-the-box thinking, Princess Zoé's closest, invisible advisor that's never mentioned), and you play her story. Like the Anno games above, the player is allowed to choose a user picture and this is used as your character icon in non-story games, but there is no explicit choice of gender.
The game allows the player to choose between male and female at the start (there's little to no character creation; you have no physical form in this), but the game assumes you to be male and refers to you as such in the story. I'm not sure if this extends to non-story modes, but I assume so as it seems to be errors caused by translation.
The Elder Scrolls V: Skyrim
The player is allowed to play as male or female and customise their character as they see fit. There are no real gameplay differences between male and female, but the game's NPCs (non-player characters) react to the player character's gender from time to time.
As I've hopefully shown, these games allow for some choice of gender, typically with no bearing on the gameplay. There are a few games in which you're punished for playing a female character, such as Mount & Blade: Warband, but these tend to be few and far between.
Which of those above is my favourite for gender? Well, I'm going to have to say The Settlers VII. It has a mix of female and male fixed campaign characters, but it doesn't let gender be any judge of character. Zoé is shown to be more capable than most other characters, with the story mode actually pitting you against a king, an ex-king (I know) and someone else in the final mission. I don't think it's perfect, though. There's a distinct lack of female settlers, with most of those shown in-game being male, although I'd also say it doesn't entirely fall into the trap of "women's jobs", in that some of the female settlers are doing things like carrying goods around (including wood, ore, etc). There are no female soldiers, however, and I've not yet encountered any female generals for hire in the tavern.
But I still love the game. It's not afraid to have a female protagonist (and there's even a female antagonist at one point), but it doesn't make any song and dance about it. Zoé's success in the end is impressive because she, as a young person with little experience in the world, overcomes betrayal, lies and her own over-eager attitude and takes what she sees to be rightfully hers, and also to free a people from its oppressive leaders. Her gender has nothing to do with it. Heck, she's a princess who wears trousers.
The Elder Scrolls V: Skyrim also does it fairly well, but... I think it misses the mark a lot. The player's gender has little bearing most of the time, nor does the player's race... and that's where it falls flat on its face. It's a world with - if you pay attention to the storyline - a lot of racism, discomfort and social troubles. If you play a Khajiit or an Argonian, two of the most oppressed and disliked races according to the in-game lore, you're not subject to much beyond a few repeated comments from the game's NPCs. No-one mistreats you, though, there's no "Oh, you're a Khajiit? Get out of my shop you thieving, flea-infested cat", as an example. It feels very shallow. Obviously there's reasons for that (not wanting to block players from content, for example), but I do wish the game was a little more perceptive and reactionary.
It even manages to, mostly, avoid gendered armour (mostly). There's a lot of breast covering, as one might expect, but if a male piece is topless then the female piece will be not far off that. The armours generally worn by bandits (Hide, for example) will be little different between the genders. There's a lot of pieces like the Dwarven armour (see above) which too is fairly gender neutral. But some pieces do it wrong, because Bethesda can't keep away from Boob Plate armour. There's the Steel Plate armour, the very exposing Falmer armour and some pieces such as Orcish adapt slightly to the female form, much to my annoyance. There's nothing wrong as such with mildly feminised armour, but often it's taken too far (such as the steel plate) and becomes - realistically - dangerous to the wearer. I understand that this is a fantasy game, but both Oblivion (the previous game in the series) and Skyrim have a heavy dose of realism to their art styles, and as such the aesthetics of the armour should reflect that.
But then we get to games like Patrician IV and The Settlers VI, which manage to do it wrong. If you're a faceless, omnipotent player, the game should not gender you if there's no real choice in who you are. The cutscenes should not refer to me as him or even her, because I've had no input in that and the game has not told me who I am. Even worse is Patrician IV's situation, in which it refers to you as male despite being allowed to choose your gender. This might be poor scripting, it might be something else, but I find it really poor. This contrasts with The Settlers VII which allows the player to choose a female user picture, but does not gender the player with that choice.
I guess what I'm trying to say is this. If a game allows the player to choose their gender, there are two ways to go about it, either way being equally valid, and they are to either let it have a noticeable impact or none at all. If the game world is gender neutral, then there should be no impact beyond pronouns. If it's not, there should be a bigger impact. But if you're letting the player choose the gender, make sure any gender-based reactions are correct. If you have references to the player as "him", make sure that upon choosing female they are "her", because otherwise it negates the choice. Why allow the player to choose if you're just going to ignore said choice?