Game mag John distributed (7)
I believe the answer is:
mahjong
'game' is the definition.
(mahjong is a kind of game)
'mag john distributed' is the wordplay.
'distributed' indicates anagramming the letters.
'mag'+'john'='magjohn'
'magjohn' with letters rearranged gives 'MAHJONG'.
(Other definitions for mahjong that I've seen before include "Chinese game using tiles" , "Chinese tile game" , "Game of Chinese origin played with tiles" , "Game played with pieces called tiles" , "Chinese table game" .)