Crossword Genius

Hotel contributed to rustic game (8)

Ross

I believe the answer is:

pheasant

I'm a little stuck... Click here to teach me more about this clue!

'game' is the definition.
(I know that pheasant is a type of phasianid)

'hotel contributed to rustic' is the wordplay.
I cannot quite understand how this works, but
'hotel' could be 'h' (phonetic alphabet: alpha, bravo, charlie etc.) and 'h' is present in the answer.
'rustic' could be 'peasant' (peasant is a kind of rustic) and 'peasant' is located in the leftover letters.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for pheasant that I've seen before include "Colourful game bird" , "Game-bird" , "Ant heaps (anag.)" , "Long-tailed gamebirds, male has bright feathers" , "Cock" .)

I've seen this clue in The Times and The Sun.
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