Here it is in French in 1788, as "The Twelve Questions" but still beginning with the question animal, vegetable, or mineral: https://www.google.com/books/edition/Les_soir%C3%A9es_amusan...
Here it is in English in 1796, as "Game of Twenty": https://www.google.com/books/edition/The_Juvenile_Olio_Or_Me...
I haven't looked too hard for earlier examples in other sources. I see Sorel had a game called the Game of Questions in the 1600s, but it's pretty different: https://wobbupalooza.neocities.org/