American’s game and, without question, profligate (5)

I believe the answer is:

roque

'american's game' is the definition.
(US croquet variant)

'without question profligate' is the wordplay.
'without' means one lot of letters goes inside another.
'question' becomes 'q'.
'profligate' becomes 'roue' ('roue' can be a synonym of 'profligate').
'q' put inside 'roue' is 'ROQUE'.

'and' acts as a link.

(Another definition for roque that I've seen is " US court game".)

I've seen this clue in The Times.

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