The most common and most likely answer to this crossword clue is the 5 plus 5 letter word RUGBY FIVES
I've seen this crossword clue in The Times
R
U
G
B
Y
F
I
V
E
S
More clues leading to the result RUGBY FIVES
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 = rugby fives.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.