There's not much to add that Matthew hasn't already covered, but to place particular focus on the case of Dungeons & Dragons - I think that that game (the offspring of the older wargames which HG Wells famously loved, as well as the "father" of modern role-playing games) is a case-in-point on the preeminence of the Protestant / Puritan perspective in the American moral compass. The infamous Jack Chick comic tract "Dark Dungeons" seems to have been the flashpoint for the religious opposition to the game. The central conceit of the tract seems to be that D&D necessarily leads to real-life witchcraft and devil worship due to the usage of magic and wizardry in the game. It's very much like the Puritan opposition to Halloween - a scrupulous over-reaction to superficial aspects with no real analysis of the thing per se, as a whole, or in context.
I've heard condemnations of Tolkien by these same Puritanical types, on the same scrupulous and superficial grounds. And the settings and character types of D&D are nothing if not warmed over Tolkien (with perhaps a dash of Robert E. Howard). The game, in itself, is, like most other games, morally neutral. It can, or course, be situationally sinful, as any other neutral activity can be, but, in moderation, it can be a useful tool for strengthening mathematical skills, imaginative powers, strategic thought, and, inasmuch as it fosters an interest in Tolkien, can open players up to the works of the 20th Century's greatest Catholic literary figure. Thus, I was perplexed to learn that there apparently exists a pamphlet for examination of conscience, issued by the FSSP, I believe, which categorizes playing Dungeons & Dragons (specifically, by name) as a mortal sin. From what I recall of the text quoted from the pamphlet, the reasons given for the sinfulness of the game were the same tenuous connection to witchcraft posited in the Chick tract. As I've said before, since the Puritan model of piety and morality is the prevailing one in America (and most of the Anglophone world in general), well-meaning American Trad Catholics inevitably fall into using the Puritan's moral yardstick as the de facto standard. I was surprised to learn, however, that that influence could get as high up as a pamphlet published by the FSSP.
Catholic parents should, of course, strictly filter and monitor what their children consume. And that brings to mind the main secular force behind the moral panic against D&D in the 80's - a woman named Patricia Pulling. After the ѕυιcιdє of her teenaged son, she learned that he was an avid player and collector of D&D manuals and paraphernalia. But, by her own admission, she had had "no idea" what D&D was until after her son's death. That ignorance bespeaks a mother (and, presumably, and more importantly, a father) entirely disengaged from their child's life and interests. It is that disengagement which, I would argue, is the crucial element to blame for their son's tragic end. Mrs. Pulling's entire passionate campaign against the game and its publisher (which she waged until the end of her own life) strikes me as a protracted quelling of a guilty conscience desperate to pin her own complicity in her son's ѕυιcιdє onto a convenient scapegoat.