I can only guess. as if they were merely playing a game of tiddlywinks, which is not a serious game. "with flippancy" might indicate that the third element in any game of tiddlywinks is flippancy, thus the personification.
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Clive
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No one ever plays tiddlywinks without someone being flippant.
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After reading the first sentence, I conclude that everyone plays tiddlywinks seriously.