One could argue that poetry itself is a game. Many poems certainly play games with their readers, and poets often use games as a metaphor: Paul Farley's piece on Monopoly is a personal favourite. Other genres, meanwhile, also get involved: Julio Cortazar has a terrific novel called Rayuela (Hopscotch), which invites the reader to tackle it in one of two ways - as a linear progression from start to finish or by playing hopscotch, jumping from one chapter to another as per his instructions. The concept's brilliant, but the execution is better.
Very much in that tradition, Maria Taylor has an intriguing set of poetry bingo cards out from HappenStance Press. The website explains them as follows:
"These cards (essential apparatus for readings and festivals) will encourage completely the wrong sort of concentration, possibly even an inappropriate response (BINGO!).
The set of four different cards can also fulfil a useful slot in terms of entertaining postcards for poetry friends. A5 in size, they contain the key words on the back as well as plenty of space to scribble messages, poems or aphorisms.
In terms of extreme left-field writing, each card is a poem in itself."
I'd not only pay good money for the cards themselves (three quid, see the link here), but even better money to be in the audience while certain poets played with them!