That game is peculiar, good gracious! (5)
I believe the answer is:
rummy
'that game' is the definition.
(rummy is a kind of game)
'peculiar good gracious' is the wordplay.
'peculiar' becomes 'rum' ('rum' can be a synonym of 'peculiar').
'good gracious' becomes 'my' (I've seen this in other clues. I am not sure about the 'good' bit.**).
'rum'+'my'='RUMMY'
'is' is the link.
Can you help me to learn more?
(Other definitions for rummy that I've seen before include "Gin perhaps?" , "Odd; card-game" , "Two-pack card game" , "Set, sequence card game" , "with an alcoholic taste?" .)