And does it work because of stopping sweating or clogging pores, which is what people antiperspirants do? If so, it would not work on a dog, since they don't sweat like people.

I don't know what people do with stinky dogs when they can't bath them. Is there a dry shampoo?

There are all sorts of non-bath solutions for stinky dogs. A very light dusting of cornstarch - NOT talcum - or a brief spray with well diluted vinegar, or official dry or waterless shampoo, etc. It's just that the idea of MOM had never crossed my mind. The brewer's yeast they get helps against smell AND fleas.

I bought some for my Rottweiler (now in doggy heaven) because I could not coax her into the bathtub. So in cold weather, I used it for her. It is called Magic Coat by Four Paws. I think I bought it at Petsmart.