Game John edited in periodical (3-4)
I believe the answer is:
mah-jong
'game' is the definition.
(I've seen this before)
'john edited in periodical' is the wordplay.
'edited' indicates an anagram.
'in' indicates putting letters inside.
'periodical' becomes 'mag' (short for magazine).
'john' anagrammed gives 'hjon'.
'hjon' put into 'mag' is 'MAH-JONG'.
(Other definitions for mah-jong that I've seen before include "Chinese tile game" , "Game played with pieces called tiles" , "Chinese game with winds?" , "Game of Chinese origin played with tiles" .)