The most common and most likely answer to this crossword clue is the 4 plus 2 plus 3 plus 6 letter word PUSS IN THE CORNER
I've seen this crossword clue in The Times
P
U
S
S
I
N
T
H
E
C
O
R
N
E
R
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 = puss in the corner.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.