Их работа — закрывать магазин.

English Translation

Their job is to close the store.

this means closed not close to?

Yes, “закрывать” is the verb “to close” (as you can tell by the ending “ать”, which indicates the infinitive of a verb). Its meaning is not related to the adjective “close” (as in “a close friend”) or the adverb “close to” (as in “they live close to the train tracks”).