Nuka-Cola Vending Machine's last ability triggers whenever you sacrifice a Food for any reason, not just to activate a Food's activated ability.

If an effect refers to a Food, it means any Food artifact, not just a Food artifact token. For example, if you sacrifice a nontoken Food artifact, such as Candy Trail from the Wilds of Eldraine set, Nuka-Cola Vending Machine's last ability will trigger.

Food is an artifact type. Even though it appears on some creatures, it's never a creature type.

Whatever you do, don't eat the delicious cards.

You can't sacrifice a Food to pay multiple costs. For example, you can't sacrifice a Food token to activate its own ability and also to activate Maraleaf Rider's ability.