The most common and most likely answer to this crossword clue is the 9 plus 9 letter word EMOTIONAL BLACKMAIL
I've seen this crossword clue in The Guardian
E
M
O
T
I
O
N
A
L
B
L
A
C
K
M
A
I
L
More clues leading to the result EMOTIONAL BLACKMAIL
Buddy explains!
The straight part
We know that "children’s favourite game?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case children’s favourite game? = emotional blackmail.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.