On the whole "games are for kids" thing, I think there's fault to be found both inside and outside the gaming "community" for that perception.
Outside gaming, we all know who to blame: the crusaders and parents who instantly think games like Saint's Row or CoD are as much "for kids" as Mario and Kirby, and then get shocked and appalled when their 10 year old is screaming slurs and obscenities into a mic at a stranger on the other side of the country while beating a hooker to death with a giant purple "object". They don't bother to look at the box of any game past a cursory glance or notice the rating stamped on it and buy it for their kid anyway, or they just give their kid money and let them buy whatever they want. Nine times out of ten it'll be the M-rated game because they understand the rating system better than their parents and they know that's the game "for grown-ups". Of course, there's a bit of fault with the kid for manipulating their parents, and further fault with the parents for giving in to the kid, too.
But there's some fault with the industry and the community as well, for blurring the lines, if you will, in terms of what is for kids or adults, not being very good at making our case against ignorant parties, and turning into a selfish, exclusive clique.
On the third point (the clique thing), MovieBob makes that point well in two of his videos: Game Overthinker Ep. 59 "Bat-Slap" and The Big Picture "Words for Nerds". To add to what he says, I'd like to say that we can't expect those ignorant people to even want to try "our games" if we spend all our time trash-talking them when we're not gaming. If we sit there and act as holier-than-thou about games as we think they act, and then demand they see our point and play our games, in abbreviated words it comes across as us saying to them "Shut up and play this, then leave us alone, you lowlife piece of shit scum." Who would want to give credence to a group that acts like we do towards them?
And that brings me to point 2: if we want to be seen as more mature, we have to act more mature in how we respond to ignorance. While a minority of crusaders against gaming do so because they just hate games, a lot of people do it because they are genuinely concerned about the access children have to Mature games. That's what leads to things like the now-dead California bill and the Australia ban. The problem is that when arguing against those kinds of things, we craft all our arguments as if we're talking to Jack Thompson (who just hates games) rather than Leland Yee (a member of the "Think of the children" crowd). We get so wrapped up in defending the medium in general from the extreme minority of detractors of games that we lose sight of the concerns of people who just don't want kids playing M-rated games, and we never address how to go about alleviating those concerns without banning games. What I mean is, the way we make many of our arguments makes us look like we want kids to play these games, even if it's not true at all. For example, I don't think many people on "our side" of the California debate made it clear that the methods, not the goal, of the law were what gamers were really protesting, and that makes us come across as immature. It certainly doesn't help when we fill our arguments with crude humor and ad-hominem insults, either. Seriously, putting a dick joke in a legal argument is NOT mature. But anyway, people like Yee want the industry to do more to keep adult games out of children's hands, and if we agree that kids should not be playing those games, we have to make that clear to them when discussing it, rather than getting rude and vulgar and dismissing them entirely. Proposing an alternate solution would help. One such compromise I see here in Japan is organizing games in stores by rating without a "back room" for adult games, and some stores keeping 18+ rated games in a still-visible case so that people can see it but have to specifically ask the cashier for the game if they want it. No confusion there!
For my last point, the blurring of the lines, what I mean is, look at how games tell stories and how they're advertised. Many of us want games to be seen as an art form worthy of telling powerful stories and conveying profound messages that could truly be called mature. In the sea of games that have tried, the successes have been few and far between. Often games end up getting their message lost in other more entertaining aspects of the game, or the attempt was there but the message itself was quite shallow, or the conveyance of that message was executed poorly. When a game does succeed, rare as it is, how is it usually advertised? You know. BIG-ASS GUNS (or swords)! BIG-ASS EXPLOSIONS (or dragons)! BIG, HOT ASSES! Does that look very mature to you? That's a 13 year old boy's idea of maturity, because that's who the game is being advertised to. If we want to be taken seriously and get people to stop thinking games are just for kids, we have to stop targeting kids, even teenagers, in marketing campaigns for adult games. If a game wants to be taken seriously for truly mature themes, and not just violence and sex, the publisher needs to present the game in a way that will get that point across. One other thing to point out is that the PS3 and 360 are flooded with M-rated games dedicated to this adolescent idea of maturity being all about an overload of sex and violence in the media they enjoy. Which is OK: those kinds of games are good fun. Just don't expect anyone to take us seriously for holding them up as examples of quality in the medium.
So that's my diagnosis of gaming being "for kids". It's as much "our" fault as "theirs".