The most common and most likely answer to this crossword clue is the 7 letter word BOWLING
I've seen this crossword clue in The Guardian
B
O
W
L
I
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G
More clues leading to the result BOWLING
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 = bowling.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 BOWLING mean?
BOWLING verb- To roll or throw (a ball) in the correct manner in cricket and similar games and sports.
- To throw the ball (in cricket and similar games and sports).
- To roll or carry smoothly on, or as on, wheels.
- To pelt or strike with anything rolled.
- A game played by rolling a ball down an alley and trying to knock over a triangular group of ten pins; ten-pin bowling/five-pin bowling
- Candlepin bowling.
- Any of several similar games played indoors or outdoors.
- The action of propelling the ball towards the batsman.
- A particular style of walking associated with urban street culture.
- (gerund) The action of the verb bowl.
- Road bowling.