Eating halal food

Where does it imply or say in this verse that you have to make sure that they slaughter the animal according to their religion and pronounce the name of one God ?
In fact it does not mention slaughtered animal it gives an open license to eat from their food. Since eating pig is strictly and explicitly prohibited in other verses so I take that exception.
If they believed in one God then there will be no segregation between Muslims and People of the book . Will they be not classified as Muslims ?