The most common and most likely answer to this crossword clue is the 7 letter word PINBALL
I've seen this crossword clue in Financial Times
P
I
N
B
A
L
L
More clues leading to the result PINBALL
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 = pinball.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 PINBALL mean?
PINBALL noun- (games) A game, played on a device with a sloping base, in which the player operates a spring-loaded plunger to shoot a ball, between obstacles, and attempts to hit targets and score points.
- The ball used in pinball.
- A situation where a ball is frantically kicked between many players.
- To dart about rapidly.