I picked "Unsure."
Honestly, I'd say "A little," but that most stories that get published (whether they are videogames, movies, television shows or books) are or can be construed as a little bit sexist.
Think about it for a minute. Really think about your favorite games, shows, books and some of the common tropes done with females and males (and those in between, in rarer cases). I've been going over old episodes of a onetime favorite show of mine, "The X-Files" and reading a cute fancomic "cartoon recap" someone did of the series. I laughed at their joke "SCULLY IN PERIL!" on one panel and the jokes made toward the "Scully in peril" episodes. Now, "The X-Files" was a show noted for having a STRONG female co-protagonist. Scully shoots things. She's killed people in the series. She is a competent, science-minded FBI agent who was written, specifically, to flout certain stereotypes about women (she's logical rather than emotional, is the sane-anchor to her highly intuitive male partner), and yet... she's a damsel in distress about every other episode. (Sure, she's saved Mulder a few times, but the sheer number of "Scully in peril!" episodes is the stuff of fandom jokes.
Or, you know... I haven't played much of "Metroid," but I've read the complaints people have of what happened to her character in "The Other M."
Bada$s women who get weepy or imperiled on a regular basis...
Then, there's the other side of it. I found myself reluctantly kinda-sorta agreeing with a (male) book-reviewer on a blog once when it came to female protagonists in Young Adult literature. I prefer Meg Murray from "A Wrinkle in Time" and how real and awkward she was, yet able to save her family through peaceful means to what the guy called the "Katniss Syndrome" of modern YA literature. That is, he was criticising Katniss Everdeen of "The Hunger Games." I defended Katniss a great deal when I posted a reply to this blog, because I thought the reviewer was being a bit unfair, but I actually agreed with some of what he was getting at: the female characters who are made uber-bada$s to "make up" for the "damsel syndrome" that is traditional, and to try to attract the attention of young male readers so as not to confine the fanbase to "girl lit."
So, really, you're either damned if you do or damned if you don't. Damels are sexist, but most people see uber-overcompensating bada$sery as over the top and not real and "sexist" in a different way.
The world is still ruled by men, too. I mean... there is a reason why Rowling wrote "Harry Potter" and not "Harriet Potter," and why the team behind "Avatar: The Last Airbender" had some reservations when creating "The Legend of Korra." (Hopefully, the *surprising* widespread love of a female protagonist who tends to self-rescue will teach the entertainment industry something).
I myself, have run into this in regards to the writing/publishig industry. I keep my pen-name to initials (not just because I think it looks classy) but because I was unfortunate enough to be given a very "feminine" first name by my parents. (My name is actually unisex and there are some famous men who've had it, but it is mostly a female-name in our current culture). I don't want publishers and agents to know I'm a woman right off the bat (because some will still reject you over that crap). I once got a rejection letter for a novel I wrote about a protagonist who saved a magical land, wielded a sword and led armies - because, and I quote "We are looking for a heroic protagonist." The main character of that tale was a woman. My fiancee' tells me that "heroic" is literary-agent code for "male." This was only a few years ago. This stuff happens in our world.
So, you know, I'm not surprised that "damsel stories" are still popular. I tend to gloss over them, myself, in the case where the story is good (or in the case of LoZ, the game is just darn fun to play), because I just expect this thing to still happen. Even the "progressive" parts of the entertainment industries are prone to a little sexism by nature just because it's gone on too long. Maybe it will go away when all those who are growing up right now on "Legend of Korra" are running things and all the old guard are retired or dead.
Now, this makes it sound like I'm only complaining about sexism, including the sexism of LoZ's "damsel" stuff. Well, I hit "Unsure" for a reasons.
LoZ suffers from the classic "fairytale" "damsel in distress" stuff in spades, but it's actually made some good strides in a more progressive direction. Zelda is shown to have a lot of magical and spiritual power, and she sometimes takes an alter-ego form in which she goes forth and fights evil herself, rather than relying *solely* on the Chosen Hero. She'll fight from the shadows, or skewer Ganon with missile-sized light arrows, or just spend half a game looting and plundering random ships as a crazy pirate. Then, there is Midna, who seems to be running the entire show in Twilight Princess. I do think she is overly concerned about her looks as an imp, especially when she has so much super-kill-weapon!magic power with her freakin' hair and the fused shadows. The world is ruled by Goddesses and women are consistently shown to have a lot of wisdom and magical power, moreso than the protagonist and many of the male NPCs... then again, that plays to certain "women as sorceresses" stereotypes, too...
Eh. Damned if you do, damned if you don't. The way society is and has been, and with the emergence of the startling idea of it beginning to even *consider* that my gender might deserve rights, pretty much anything and everything anyone does (even if they are a female writer/director/creator) is going to be considered "sexist" in some way.
If you're concerned about formula, read stuff on TV Tropes, put something you're working on through the Betchel Test, if you're not female, talk to women... etc.
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