One drink like another? Two can play at that game! (3,5)
I believe the answer is:
gin rummy
'that game' is the definition.
(card game)
'one drink like another? two can play' is the wordplay.
'one drink' becomes 'gin' (gin is a kind of drink).
'like another? two can play' becomes 'rummy' (I can't explain this - if you can you should give a lot more credence to this answer).
'gin'+'rummy'='GIN RUMMY'
'at' acts as a link.
Can you help me to learn more?
(Other definitions for gin rummy that I've seen before include "Card game" , "cards" .)