The most common and most likely answer to this crossword clue is the 11 letter word VINGT-ET-UN
I've seen this crossword clue in The Guardian
V
I
N
G
T
-
E
T
-
U
N
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 = vingt-et-un.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.
What does VINGT-ET-UN mean?
VINGT-ET-UN noun- The card game pontoon.