Group organising games involved in snack food (7)

I believe the answer is:

tapioca

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'food' is the definition.
(tapioca is a kind of food)

I cannot understand how the rest of the clue works.

(Other definitions for tapioca that I've seen before include "Starch from cassava used in making puddings" , "dessert" , "Starchy dish" , "it thickens" , "Substance from cassava used to thicken puddings" .)

I've seen this clue in The Telegraph.

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