The article is skewed somewhat. Actually at issue is that a D&D group violates prison rules on congregation of inmates. Although this particular case calls out roleplaying in particular, the same rule applies to any organization with in a prison: book clubs are likewise forbidden, and no activity that would place one prisoner in a position of authority over others is permitted.

Disclaimer: I am in no way associated with a prison or any employee or inmate thereof, so I don't have any special insight. This is the information I gained the last time this issue was in the news, some seven or eight years ago, supplemented by a recent conversation about this same article on the Christian Gamers' Guild this past week.