In this particular case, they were not referring to the ditziness being a game. They were referring to the game they were in fact playing The Amazing Race.

You're right, though, a pure example may only exist in the laboratory (as that one could be taken to mean that their acting ditzy was the game).

It's not quite a case of non-sequiturs occuring. The irrelevant-disjunctive must be something that the speakers think are relevant together, but aren't.

;-)