A game on board for animals (5)

I believe the answer is:

stags

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

'for animals' is the definition.
(stag is a kind of animal)

'a game on board' is the wordplay.
'a game' becomes 'stag' (stags are game in the hunting sense).
'on board' becomes 's' (I can't explain this - if you can you should believe this answer much more).
'stag'+'s'='STAGS'

Can you help me to learn more?

(Another definition for stags that I've seen is " Male deer".)

I've seen this clue in The Globe and Mail.

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