In American English, store means shop.

The preposition Aus takes the dative, and Laden is masculine, so the definite article dem informs you it is a singular shop.

If it had beeen plural, shops, then it would have been Aus den Läden. Note the umlaut, changing the pronunciation for shops.

"Off the store" makes no sense in English.

I think you can use "off the store" only in a sentence like "it's the street off of that store". But maybe even that is colloquial or incorrect... anyways, you can only have something from a store.