Chicken I could see like actual game chicken of pushing someone to the edge until they tap out.

Maybe like... Having the 2nd highest amount of something.
Suggesting the 2nd longest word, the 2nd most vowels etc.

You wanna get as much as you can but not all the way, because you're the chicken.

Definitely could easily translate nonsensory to a board game. Both the text prompts and the drawing prompts.

Teams could be a fun way to do it.
Have a designated person to answer the question first and everyone else open votes and they can be swayed to conform or not. Points given based on how close to the same answer they get. We could have two threads going at the same time. Or we can just have a rotating cast of who leads until everyone has a go. That would definitely make the game run for a while though.