The most common and most likely answer to this crossword clue is the 7 plus 7 letter word TRIVIAL PURSUIT
I've seen this crossword clue in The Guardian
T
R
I
V
I
A
L
P
U
R
S
U
I
T
More clues leading to the result TRIVIAL PURSUIT
Buddy explains!
The straight part
We know that "Game" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case game = trivial pursuit.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.