How the game was played
The first person would sing a line of the lyrics and the rest would repeat back. This would proceed through the number of days with the accompanying increasing number of items for each day to test each person's recall. The person who made a mistake or forgot one of the lines had to pay a forfeit such as giving a kiss or a candy.
The earliest known version first appeared in a 1780 children's book called Mirth With-out Mischief. From 1760 in France , there are earlier editions of the same song which support the fact that the song was not of English origin.
Maybe next year...
In any event, The Twelve Days of Christmas remains a popular song at Christmas time. Maybe next year, you should try it as a Christmas party game for some good-hearted revelry in the Season of Christmas.