I'm following you, but the language pertains to "crops, livestock, livestock products, or other agricultural products that are intended to be sold, labeled, or represented as 100 percent organic, organic, or made with organic (specified ingredients or food group(s))"
It looks like you can't have a USDA certified organic t-shirt, but you can have a t-shirt made with certified organic cotton. It looks like you can't have a USDA certified organic shampoo, but you can have a shampoo made with certified organic ingredients. Technically, it looks like you can't have a USDA certified dog food, but if a dog food lists it's crop or livestock ingredients as organic, then it is regulated under the NOP. Although I have seen the dog food with the USDA seal.
Since the laws only pertain to these specific products I guess technically you could have a dog food without any organic products listed in the ingredients, but with a big "ORGANIC DOG FOOD" label on it, since the laws wouldn't apply otherwise.