Entertainment venue playing REM etc ad nauseam? (9,6)

I believe the answer is:

amusement arcade

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'entertainment venue' is the definition.
The definition suggests a singular noun which matches the answer.

'playing rem etc ad nauseam?' is the wordplay.
'playing' indicates anagramming the letters.
'rem'+'etc'+'ad'+'nauseam'='remetcadnauseam'
'remetcadnauseam' with letters rearranged gives 'AMUSEMENT ARCADE'.

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(Other definitions for amusement arcade that I've seen before include "gambling joint" , "kids might have fun here" , "Where to find games machines" , "gambling haunt" .)

I've seen this clue in The Times.

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