The most common and most likely answer to this crossword clue is the 5 plus 5 letter word STRIP POKER
I've seen this crossword clue in The Times
S
T
R
I
P
P
O
K
E
R
More clues leading to the result STRIP POKER
Buddy explains!
The straight part
We know that "The divestment game?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the divestment game? = strip poker.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.