The game is of trifling significance (9)
I believe the answer is:
bagatelle
'the game' is the definition.
(bagatelle is a kind of game)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for bagatelle that I've seen before include "Trinket - game played on a board with balls" , "Something trivial" , "piece, one for piano" , "Musical item" , "Unimportant thing" .)