Twister was a board game. The Second Doctor brought it to the Christmas party hosted by the First Doctor. (PROSE: The Feast of Seven... Eight and Nine)
While meeting Clara Oswald's parents and Clara Oswald's gran for the first time while naked, the Eleventh Doctor asked if anyone wanted to play Twister. Clara's gran showed interest in the offer. (TV: The Time of the Doctor)
In 2025, the Fifteenth Doctor and Anita Benn played twister at least once as part of their regular "chair night" activities. (TV: Joy to the World [+]Steven Moffat, Doctor Who Christmas Special 2024 (BBC One and Disney+, 2024).)
Behind the scenes
Information from invalid sources
A Cyberman played Twister with the Eleventh Doctor and Amy Pond at a Christmas party. (NOTVALID: Consider Yourself One Of Us...)