Honestly I don't even think of this as a "trope," or anything, but any time escape rooms are mentioned in some show I'm watching, I just get an urge to make a list of the references I've heard to them, if I can remember them all (which I probably can't). So... I'm finally starting such a list.
The Big Bang Theory (TV)
2015: In the season 8 episode The Intimacy Acceleration, Raj, Emily, Leonard, and Amy visit an escape room.
The Flog (web)
2015: In the season 2 episode Room Escape, Felicia Day is joined by Clare Grant, Zachary Levi, and Seth Green in an escape room.
The Real O'Neals (TV)
2016: In the season 2 episode The Real Acceptance, Kenny, Brett, Pat, and Clive visit an escape room.
Brooklyn Nine-Nine (TV)
2016: In the season 3 episode Karen Peralta, Captain Holt plans a team-building exercise at an escape room, but only he, Gina, Hitchcock, and Scully show up.
Castle (TV)
2016: In the season 8 episode The Blame Game, Castle, Beckett, and others are abducted and put in separate rooms where they must solve puzzles if they want to survive. For real. (I was hesitant to include this on the list, since it's not really an escape room, and it's certainly not a game, but I guess it does have the same basic premise. Sort of.)
American Housewife (TV)
2017: In the season 1 episode Surprise, Katie and Greg turn their basement into an escape room for Oliver's birthday party.
Escape! (web)
2017: This is a whole webseries about escape rooms. Each episode has a different group of celebrities working together to solve a different escape room.
My Little Pony: Friendship Is Magic (TV)
2017: In the season 7 episode All Bottled Up, the Mane Six visit an escape room.
Bob's Burgers (TV)
2018: In the season 8 episode The Trouble with Doubles, Bob and Linda go on a date with another couple, and end up visiting an escape room.
Modern Family (TV)
2018: In the season 9 episode The Escape, Phil, Cam, and Gloria plan to go to an escape room, but accidentally get locked in an ordinary basement... from which they have to escape.
My Little Pony: Best Gift Ever (web)
2018: One of three webisodes that tied in to the TV special "Best Gift Ever" was called "The Great Escape Room," and involved what is probably the least professional, most nonsensical escape room ever devised.
Just Add Magic (web)
2019: In the season 3 episode Just Add Codes, Darbie's new friend Piper invites Darbie, Kelly, and Hannah to join Piper and some other friends at an escape room.
Single Parents (TV)
2019: In the season 2 Halloween episode "Welcome to Hell, Sickos!" Will plans to briefly attend his girlfriend's birthday party before going to a pumpkin carving contest his daughter is entered in, but gets stuck at the party when it turns out to include an escape room.
Date Night (web)
2019: In the episode Can Kim Possible Escape the Room?!, Christy Carlson Romano and her husband, Brendan Rooney, do a Harry Potter-themed escape room together.
DC Kids Show (web)
2020: In the episode Batman Escape Room!, the Joker locks Jett and Nandi in their respective bedrooms, and leaves a series of clues for them to find the combination to the padlocks on their doors.
The Unicorn (TV)
2021: In the season 2 episode No Exit, the gang visit a spy-themed escape room.
Pretty Freekin Scary (TV)
2023: In the season 1 episode The Power of Life, the Grim Reaper tasks Frankie with going to an Underworld-themed escape room, but she passes the task off to Pretty and Scary. Frankie has to go to the escape room herself in the next episode, Life As We Knew It.