If roleplaying is making decisions as if you were a different character, then I don't rp in board games basically at all. To me, board/card games are most fun when everyone is trying their hardest to win. Roleplaying kind of gets in the way of that. In ttrpgs, the goals are more open, and roleplaying fulfils one of those goals. The difficulty of challenges is also much lower, so there's room to make "unoptimal" decisions because you're playing a character, without getting everyone killed.
In video games, I will maybe occasionally, but not much. The closest thing I can think of is that in Fe3h, I always paired Byleth up with a teacher or faculty, because it seemed creepy for a teacher to get romantically involved with a student.