Rowling knows just enough about TTRPGs to think that they're both deeply uncool (she is at her heart, a "mean girl", even by her own self-serving 'poor little me' accounts of her time a school, she was part of a mean girl clique), and to get very angry at the idea of someone potentially roleplaying characters from her novels but outside her control. This is a woman, who when only the first two HP novels were out, semi-famously gave an interview in a widely-read British magazine (I forget which) where she basically got into a fight with the interviewer because the interviewer took-as-read that HP was fantasy (which it undeniably is!), and asked about Rowling's fantasy influences, and Rowling absolutely excoriated fantasy literature, saying HP was definitely not that, and that fantasy was basically just wank-material for spotty fat dim 13-year-old boys (barely paraphrasing and I 100% believe that was her genuine "mean girl" opinion, given the sort of school she went to). Much later she changed her mind on this (about when four or five books were out I think) because she realized how much her readers crossed over with general fantasy readers (like, huge crossover) and that maybe insulting them directly wasn't a great plan.
And remember she also only through gritted teeth barely tolerates HP fan fiction, and I strongly suspect if she could legally shut it down now without blowing up the brand, she would.
I think the core issue for her is not just that TTRPGs are for losers, but more "nobody should be allowed to RP any characters I created, without my explicit permission". To her, videogames are mostly safe because they are simply retellings of her works, or don't really feature her actual characters/story, just HP branding. This is, I think, how the most recent HP game, the big one, I forget the name, got away with it, it's set deep in the past of Hogwarts, and doesn't really feature main HP characters as a result. So even though it's a lot more like an RPG than most previous HP games, you're not going to be able to use Harry to say "trans rights" or something. Also even there the one trans character in the game has a pretty insulting name ("Ima Mann" or something equally depraved and Rowlingesque), so I suspect she made some edits.
