Game over following endless stick (4)

I believe the answer is:

polo

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'game' is the definition.
(polo is a kind of game)

'over following endless stick' is the wordplay.
'over' is an insertion indicator.
'endless' says to take the centre.
'stick' becomes 'plo' (I can't explain this - if you can you should give a lot more credence to this answer).
The central letter of 'following' is 'o'.
'o' going inside 'plo' is 'POLO'.

Can you help me to learn more?

(Other definitions for polo that I've seen before include "Game played on horseback wielding mallets" , "Marco" , "Mounted game" , "Team game played with horses" , "jersey" .)

I've seen this clue in The Telegraph.

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