The most common and most likely answer to this crossword clue is the 10 letter word SPILLIKINS
I've seen this crossword clue in The Guardian
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More clues leading to the result SPILLIKINS
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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 = spillikins.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 SPILLIKINS mean?
SPILLIKINS noun- One of the straws (or small pieces of wood, ivory, etc.) used in the game of jackstraws or spillikins.
- A game in which players attempt to remove flat, carved sticks of ivory or wood (the individual spillikins of meaning 1.) from a scattered pile without disturbing any stick other than the one currently being removed.