A big part of my book is that the characters play the tabletop RPG "Dungeons and Dragons". There is no content actually showing them playing it, but they do mention it. Would that be allowed?
If the characters talk about having played the game, rather than actually playing on-screen, as it were, the actual game is in danger of becoming an extraneous detail -- at best, it's group characterization ("This group of friends are geeks of the flavor who sit around a table with odd-shaped dice and pretend to be wizards and barbarians"). At worst, it's trend-following.
Aside from whether it's a good idea from a writing standpoint, as long as you don't say anything about the game that could be construed as defamatory (in the worst possible light -- lawyers can make "You look great today" into an actionable insult), you ought to be okay. It would surely be safer if you gave the off-screen game a different name (but these days there are at least a dozen knock-off games similar to older editions of Dungeons & Dragons, with roughly similar names, and you should avoid their names, too).
(And just so no one takes the above the wrong way, I've been one of those geeks with the dice for more than forty years.)