I can say with a fair degree of confidence that this is true. It's only an approximate measure (as with all demographic surveys, this kind of thing is skewed by selection bias, social stigmas, etc. - we're also only a tiny proportion of Neopets users), but the demographic analysis for TDN's Facebook page hovers around 79% female, with more than half of users (of all genders) aged between 18 and 34. That said, we have significant representation from all age ranges, from 13 right up to 65+ (of course this doesn't cover kids too young to have Facebook accounts).
I guess I should cover the main topic raised here first - my opinion on age is pretty straightforward, and in line with what most people here have said. As an older gamer, you should be able to play pretty much whatever game you want. What grown adults do with their free time is their own business, as long as they're not harming anyone else. Even in a community there are no rational or ethical grounds for excluding people simply based on their age. We are people, we define who we are, not an arbitrary time period between the present and a birth event. On a personal level, I know many much older gamers who get along just fine with young adults and teenage gamers. They're cool to have around. They're all unique people with different personalities. As far as I can tell, age really doesn't make a blind bit of difference, so there's no reason we should pretend it does.
Predatory behaviour is an entirely different subject from age and gaming. If you are using any communication medium (gaming included) to engage in abuse, whether sexual or otherwise, this is disgusting and wrong ethically, morally, and probably legally, and quite frankly you are a horrible person. This is true regardless of your age or the target demographic of any game you use. An older predator finding younger victims through a game made for young children is no better than a teenage predator finding similarly aged victims through a game made for teenagers, and this should have no bearing on an older gamer's right to play games marketed at younger audiences.
The question of age appropriate games for younger audiences brings a fair degree of general controversy into the mix. There are many games with mature content, be it violence, sex, or other material, that may or may not be appropriate for younger kids. There are a few very extensive and very well resourced national and international rating systems that for the most part do a pretty good job of labelling this content. They are thorough and backed by a lot of legal muscle to make sure games get rated properly. Combined with the massive amount of information available on the internet, it's not exactly difficult to figure out what is in a game and whether it's appropriate for your kid.
And that's where the ultimate issue comes in: parenting. No amount of resources poured into rating systems or game store legislation can do a parent's job for them. It is parents who are responsible for doing the research (even if it's nothing more than reading a rating label) to make sure a game is appropriate for their kids, taking into account all factors - not just age, but mental and emotional maturity, past experiences, potential future experiences, personal preferences, and so on. It is parents who are responsible for actually keeping an eye on their kids and paying attention to what influence it's having on them. It is parents who are responsible for sitting down with their kids and explaining important concepts they may need help understanding (be it sex or financial responsibility). A gaming console, computer, or mobile phone is not a surrogate parent. No rating label can understand a child like their parents can. Whether a child can handle a title meant for older audiences is very much dependent on the child, and only the child's parents are in a position to actually make the call.
tl;dr: Older gamers should be free to pick our own games, regardless of age. Young kids may need some help from their parents, and their parents should be ready to provide that help.
A brief tangent here because I (typically for me) want to put emphasis on something that should be self-evident: your ability to write computer code has zero relevance to your right to enjoy a game and participate in its community. The truly ridiculous elitist attitudes generally (I both believe and hope) come from people with trivial knowledge of some basic coding, a vague impression of what programming is, and no understanding whatsoever of actual game development. These people, just like trolls everywhere on the internet, latch onto whatever pathetic excuse they can find to feel superior to everyone else.
Heck, I'm an experienced programmer, and a darn good one, and beyond general "this is how computers work" facts and some speculation, I wouldn't dare try to speak from a position of developer authority on a game I had no insider knowledge of, let alone discriminate against other gamers based on largely irrelevant additional knowledge. I'm no game developer. Sure, I can write software. That's not the point. Just because you took Coding 101 in college and can throw together basic macros doesn't mean you're more qualified than anyone else to enjoy a game. Just because you're a graduate software engineer working for an IT company doesn't mean you understand game development in all its science, art, terror and glory. Just because you're a 40-year game industry veteran with a pedigree of outstanding titles you've helped develop doesn't make you more qualified to discuss a game than the developers and gamers making up the community around it (granted that one would lend your opinion some weight).
tl;dr: You (usually*) don't game by coding, ergo coding should not be a requirement to enjoy a game or participate in its community.
* There are some intriguing educational and concept games that actually have an element of coding as part of the game mechanics, but nothing really significant.
Ah yes, the big painful issue that's somehow still an issue. I don't think anyone here seriously believes that females shouldn't play video games, or that they're somehow less invested or competent in video games they play, so I won't belabour this point like I did the coding one. It is truly sad to see that sexism is still a major problem in the game industry and among gamers in general. And it's not just games - despite massive strides towards equality and general respect across the globe in all walks of life, sexism remains an issue just about everywhere in just about everything. It's not always obvious and it's not always deliberate, but it's still there. As Azurablue said, attitudes are changing, but not fast enough.
And here's the thing: I honestly believe that gamers do comparatively well in this respect. Ranging from religion/traditions to the film industry even to serious level-headed professionals like engineers, discrimination is rampant in the world, whether it's in how women are portrayed, what they're "allowed" to do, or in how much they're paid. Relatively speaking, gaming is one walk of life where women are fairly well accepted and respected. Most gamers are fairly savvy people who will happily game alongside men and women, and I say this knowing my fair share of gamers (granted of course that this view is skewed by who I choose to associate with). They don't discriminate because, well, aside from the English language's somewhat awkward enforcement of gender-specific pronouns, they don't really care what gender you are. And honestly, that's probably how it should be.
So why then is there the popular perception of gamers as generally immature and sexist? Well, this and many other issues link back to another deep-rooted issue with gamer communities in general (I'm hesitant to label this as a "problem", at most it's a perception problem). This is the issue of the "silent majority", or the "vocal minority", depending on which angle you prefer. Simply put, we have a few very loud people, and many, many relatively quiet ones.
Gamers are pretty vocal people. As far as the various walks of life go, we are among some of the loudest, shoutiest, most determined folks out there when it comes to making our voice heard - when we're upset. When we're content? Not so much. Emotionally charged gamers, or people simply seeking attention, have plenty of motivation to post angry, ranty, rude, or outright discriminatory content on gaming forums and social media. The calmer, more sensible gamers are generally disinclined to invest time and emotion in a discussion (especially an unpleasant one) when they could be, well, playing games.
As a result, it's ultimately the ones that shout the loudest who get heard. Sadly, it's often the case that the louder people are the irrationally angry ones, and the loudest of all are the hate groups seeking to stir up "controversy" for the most ridiculous reasons. It tends to be the case that a few people with opposing views get very upset themselves, only serving to make discussions shoutier and even more unpleasant. This occurs in everything from legitimate opposition to bad business practices, to more controversial stuff like balance debate, to completely ridiculous subjects like sexism in a modern industry where it has no right to be.
The one comforting point I personally like to take from all this is that the vast majority of gamers really aren't blatantly sexist or otherwise abusive - they just don't want to dive head-first into a crapfest. Unfortunately, this doesn't mean that the world of gaming isn't still terrible. We should be doing far better than we are today but we're not. The painful discrimination Azurablue experienced at game stores is one example. The widespread use of the term "girl gamer", as if the gender-neutral noun "gamer" is exclusively male and a special "girl" pass is needed for a woman to enjoy a game, is another. And then of course there's the sexist portrayal of female characters in many, many titles (it sells well, so studios stick to it - can you really blame them?). We may be ahead of the curve, but we're very far behind where we could be, and I sincerely hope that with a little time we can get to where we really should have been a long, long time ago. I would like to know at least one walk of life where people aren't treated as lesser beings, whether it be by age, coding ability, gender, skin colour, or any other arbitrary factors.
And well, last I checked, we didn't operate computers with our genitals.
Full disclosure: I am a male.