Where horses may be game (9)

I believe the answer is:

badminton

I believe this is a double definition.

'where horses may be' is the first definition.
(ref to Badminton Horse Trials)

'game' is the second definition.
(badminton is a kind of game)

(Other definitions for badminton that I've seen before include "Game using shuttlecock" , "One sport" , "Racket sport" , "Racquet sport" , "Court game" .)

I've seen this clue in The Guardian.

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