In all honesty, it's probably not Trump, but a publicist or intern that is in charge of his Twitter page that is trying to appeal to conservative Christian mother's.
In case you can't tell, Trump hasn't had the best publisists.
However, Trump being older, probably is out of touch and still holds the view that people had back in the 80's and 90's, that video games are exclusively marketed towards children and not adults, so in this situation he may believe that Vidya are exclusively for children and can't grasp that games such as GTA are actually being marketed towards older generations, and that there has been a culture shift regarding gamers since the 80's and 90's.
I believe that it was ruled unconstitutional to even restrict the sale of violent Videogames in the supreme Court a few years back, because trying to ban or prohibit video games becomes a freedom of speech issue, of course certain stores such as Game Stop have store policies in place, such as being 18 to buy M rated games, and showing an ID, but it's not legally mandated, I doubt even the president would have the power to ban, or even restrict the sale of violent video games.