The most common and most likely answer to this crossword clue is the 9 letter word PUNCHBALL
I've seen this crossword clue in The Times
P
U
N
C
H
B
A
L
L
Buddy explains!

The straight part
We know that "In America, game" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in america, game = punchball.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 PUNCHBALL mean?
PUNCHBALL noun- A simplified version of the sport of baseball, where players use their fists as a bat and a softer ball.
- The soft ball used in this sport.