I'm not into any video game except for the occasional Tetris, Snake or simple fun online game I play with my students, and I certainly wouldn't be into shooter games, they seem pointless and a waste of time to me. I don't have this fascination with crime, murders, violence and killing that half the world seems to have, and wouldn't get any pleasure from a game where the the objective is to kill as many people as possible. Such things are not part of my life and I can't relate to them. I like to learn things, and see things like sports and this kind of video game as a waste of time because you don't learn anything. If you don't learn anything, then what's the point? With TV, it's the same. I want to be informed and not entertained.
You seem to have a misconception, one that is rather unfortunately common and which I am quite familiar with.
Gaming is not all about simply murdering everything in sight. Nor is it without the potential for learning, or improving yourself.
What you have seen is what the media wants you to see: a spectacle and nothing more. The sorts of games you've seen are those usually used to draw players in by simply showing them flashy graphics and guns and blah blah blah... it's very similar to how TV shows do this.
However, much like TV, there is plenty out there that goes against that rather childish idea.
I'll give a quick example here:
This is Opus Magnum. Something of a puzzle game, so to speak, which focuses on creativity, ingenuity, and logic. The idea is simple: Build a machine that takes the various orbs (which represent elements or something) and constructs them into the shape that the puzzle requires. You have complete freedom to build the machine as you see fit, however the devices that generate different types of orbs are limited based on which puzzle it is. Your goal is not just to make a machine though, but to try to make an efficient one. The one in the image there is pretty fast, creating the desired shape (which gets placed in that funky thing on the far right) very quickly/rapidly. Every one of those individual moving parts you see in it must be programmed by the player to carry out their various functions with the correct timing. Correct spacing must also be used, or orbs will just collide with each other and the machine will lock up. Imagine just how much thinking and effort goes into making something like that. There are other ways to do it, too. Some players (such as myself) prefer space-based efficiency... that is, creating the machine not to be as fast as possible, but as compact as possible. However the player chooses to go about it is purely up to them, and there are no "correct" solutions... the only requirement is that you place the finished product into the reciever. Every person's solutions will be unique, and part of the draw of the game is to go back to old designs, and try to come up with new logic for them that improves them and makes them ever more efficient.
It is quite the mental challenge, and this sort of thing is fantastic for developing logical thinking skills. There are, actually, MANY games like this. Notice, there's no violence here. None. Nor is there any in the game's story. No violence, no blood, no sex, none of that. The games made by the Big Guys.... AKA, the largest publishers, the ones that make the really flashy crap... yes, THOSE will focus on violence/sex/whatever. Those dolts, like some in Hollywood, believe that those are the only things that sell. But if you actually take the time to look elsewhere, there's so much more to it than that.
However, even games that focus on other elements can still be useful. I personally love puzzles, strategy, and games about logic, but those arent the only ones I play. Allow me to show you something else:
Quite alot of moving bits there, eh? This type of game, which I'm extremely familiar with, is mostly about dodging all of the colorful lunacy that is thrown your way. Thinking fast, reacting faster, and being able to mentally process everything that is going on is the skillset used here. I do alot of this sort. I always have. I need a high level of challenge for something to hold my attention. As a result, over the years I have improved in various ways. My reflexes and reaction speed are... abnormal, to say the least. It's part of my characteristic impatience, actually. Most things are slow to me now. I can focus on many things at once, and I can mentally track many things at once. Every moving object in that video, for instance. Nothing escapes my notice. These are all quite useful abilities, in real life (particularly while driving, but they have many other applications as well). Hell, just the coordination alone is amazingly useful. These skills/abilities, they are mine mostly because of all of the gaming I've done. Obviously, not every game helps with this. But a great many do.
There's more though: That crazed monstrosity in the video? All of those colorful, intricate patterns? They're mine. I created the thing. I devised the patterns, and programmed the horrid thing to do them. It's part of my job (well, I say "job", but I do it on a volunteer basis, because I bloody well can) within the project of making that particular game. All that gaming, you see, led to one other major thing for me: An interest in computers, software, programming, and of course game design. All of which I learned on my own... not in some classroom setting. I've always been self-taught when it comes to computers, and it was my love of gaming that created the interest in the first place. I've learned many skills related to computers as a whole... all because of that.
And that's just that example. I could go on about the other things it's all given me... for example, the fact that I frequently travel, entirely by myself, something I thought I"d never be able to do. Yes, that's because of this stuff as well (dont ask me how, that's a long story). It's surprising, really, what effects a hobby of any sort can have on a person... if they allow it to happen. In my case, it has resulted in many improvements, many important events, and even many new friendships.
See? While the media may paint it all as one thing, that is not the only thing it encompasses. Nor is it the only function it can serve. Obviously, some games really ARE as braindead as they look, but.... sometimes, even in those, that's STILL not the case.
It's important to always look beyond the surface. That's something I've learned, over and over again, throughout the years. It's one of the most important lessons I've been taught as a result of being into this. And it's something I always try to impart to others, if I can.
Hm, I apologize if this post was long, but I like to try to educate people on this one if I see a chance. If it helps even one person to learn something, then it's worth it, as far as I'm concerned.