I use the Haxe language and HaxeFlixel as the engine, you may have never heard of.
Papers Please was coded in Haxe, though with openFL (formerly known as NME). I used Haxe once, and I liked it. It's a pretty smooth language, and development went quite fast for me (compiling too). I just quit it because I'm developing for desktops and (at the time) there were a few limitations that made a bit of a difference to me.
I can't really help with the main issue, but I just wanted to mention that I know from experience that violent video games actually do a bit of what I like to call the "punching bag effect" (release tensions, stress, anger, etc - and some games made me have an even greater distaste for wars in the real world!). Unfortunately, that I know of, there doesn't seem to be any studies corroborating that notion, but there are studies showing quite some other benefits from playing games in general, but maybe you already know all that.
I have some relatives (my aunt, for one) with similar opinions to your grandma's, but since they never really imposed them on me I never really argued either, so I'm a bit clueless about that... But if I had to, I might do it by, instead of arguing, trying to just ask questions, such as why exactly does she think games are whatever she says they are, and where did she get that idea from, and aren't crime rates lowering, and does she think puzzle games are bad too, and what about racing games (or whatever else you play), etc.
With carefully chosen questions you may end up leading her to realize that her opinion is unfounded and that she actually doesn't know much about games in the first place, and if she realizes that by herself, in the privacy of her own thoughts, she may eventually cut you some slack (people often admit their flaws/mistakes much more easily if they're doing it within themselves, without feeling the pressure of external scrutiny or anything that may make them feel attacked or unwilling to give in).
Although, if that's ever to work, you shouldn't expect it to be in the foreseeable future. It will depend on lots of factors pertaining to her personality that only you can consider and what questions you ask and how, but, who knows, may be worth the effort sometime. Essentially, try to leave something in the air that will make her think.
That said, if you get better results by doing things your own way, then forget everything I just said and go for it. Just see if you don't dig yourself a deeper hole by arguing too much like I used to.