The most common and most likely answer to this crossword clue is the 5 plus 8 plus 5 letter word PAPER SCISSORS STONE
I've seen this crossword clue in The Guardian
P
A
P
E
R
S
C
I
S
S
O
R
S
S
T
O
N
E
Buddy explains!
The straight part
We know that "A game of two hands" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a game of two hands = paper scissors stone.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.