No one would recommend feeding Rumensin to dogs, but I really doubt it would hurt them. Or let me put it this way, it would probably take a very very large dose (like impossible to eat it large) of that ration to hurt them.

I know guys that used to feed Rumensin in their sow ration to reduce cocci in the pigs, not legal and not recommended, but didn't hurt anyone.

They used to feed Rumensin to chickens as a coccidiostat, so we know it doesn't hurt them either.

Horses are susceptible for some reason, but I've never seen or heard that dogs are.