That's quite a mess you are and by the end you are the only one who will know what's best. I'll just try to give you what I believe are good arguments.
Please don't blame this on religion itself. I see you live in the US, which is a breeding ground for various cults disconnected from the major churces. I don't know what religion you or your parents are, and I don't care, but here in Europe none of the churches run around calling this or that a gateway to hell. What you must understand is that cults ar dependent on keeping their followers ignorant, they have to tell them "this is evil and you must stay away from it, just looking at it will corrupt your soul". They won't hesitate to downright lie to people, just to keep them afraid. I am Christian Orthodox myself and I have never heard anyone say anything about video games, good or bad. There are far bigger real concerns than video games int today's world. However, it is easier to frighten people.
Your parents won't like hearing that and it might not be the best idea to tell them what I told you, but you must understand this position. Admitting that you are right means admitting they were wrong and if the preacher has been feeding them lies it also means admitting that the person they trusted their souls to is just a an unscrupulous lier. Again, I don't know what religion you have and where their stance comes from, so take this just as a general advice.
Of course this isn't limited just to religious groups alone, any interest group will lie and create problems where none exist just to keep people ignorant and themselves relevant. Take for example the recent "Tropes VS Women", which is creating a problem where none existed. Last time I checked girls and women were
loving Super Mario, so what exactly is the problem? There is none, but interest groups will creat one and guilt trip you into obeying them.
Now, about violent games themselves. Violence is a part of human nature. Humans are carnivores and as such removing violence from our lives is unnatural. You can't change human nature, it is what makes us. Taking away violence from a person is like taking away sex (and if it weren't for sex you wouldn't exist). The key point is that violence is not necessarily a bad thing. Sports is full of violence and athletes are very healthy people. Violence can be constructive, think of all the hard working construction workers who are providing society with housing. You can't argue with bricks, you have to force them into place.
In today's world there is very little outlet for violence. Some people do sports in their free time. Some people do gardening or craft something. Video games are another outlet for violence. A fast-paced game will give you a good shot of adrenaline, something you can't get from sitting in an office all day and something your body craves. That is simply human nature, we need that just as we need our food. It is important to explain that what you are enjoying is not the act of killing, it is the action, the need for reflexes, strategy and wits (whatever applies to the games you play).
Playing video games is much better than being a slug who comes at home after work and vegetates in front of the TV watching other people do sports while drinking beer.
Another issue might be that you are playign a killer instead of, say an athlete something in a sport event or something. This one is tricky. First of all you have to make clear that none of it is real. None of the people you "killed" have ever existed, no one has died. You must explain you are aware of the difference and that implying that video games desensitize people is actually an insult to your intellect as a thinking person. Video games are being played by millions/billions of people all over the world, yet humanity is doing fine. Destructive violence against humans has existed before video games, is existing during video games and will exist after video games. If video games were actually bad, then how come those millions/billions of players haven't snapped yet?
Explain that you are not desiring to actually hurt anyone. It is just a silly fantasy, like a vacation, being someone else for a while and then returning back to normal life. It's just like traveling somewhere for vacation, that doesn't mean you will assimilate into that culture. You'll take a break from your everyday life, relax a while and then return back to where you came from. Video games are offering a wide variety of immersions, you can be a secret agent, a stealthy thief (Thief series), a hero (any RPG), a mayor (Sim City) or even a doctor (Theme Hospital). There are a lot of facettes to gaming and killing is just one. Condemning one of them without condemning the others is just hypocrisy. Show them the various facettes games can explore (the GoG catalogue is great).
Often the media will accuse video games when something bad happens, like a school massacre. This ties back into my argument about interest groups, the media sees a chance to exploit a tragedy for money and they don't care about the people involved. Oh, sure, some violent game was found in a teenager's home, but in which teenager's home will you
not find that same game? See how it works? Totalbiscuit has a very good video on this topic
https://www.youtube.com/watch?v=5uwAo8lcAC4 That's a good video to share as it explains the truth behind video game blaming. It's worth noting that video games are still a relatively young medium and as such it is still exploitable. The same used to be said about Rock & Roll music, but you can't sell that to today's old people anymore because all of them used to be the ones who were supposedly corrupted by rock music.
------------------------------------------------------------
This is really all the advice I can give you. I can give you the tools, but you'll know best how to use them. If you parents just refuse to listen to anything I'm afraid I don't know what to do. My parents used to be frightened as well because of what the mass media were telling them, but when you realize everyone around you is playing video games, including violent ones, you start realizing
you are actually the weirdo for believing this propaganda. Don't expect change immediately, the process of admitting you are wrong doesn't happen over night.
