That fourth word does not sound like a "le". It sounds more like "il", which makes no sense.
Good, if you have understood that it makes no sense with "il", then you know it has to be "le".
Aren't you not supposed to say the girl version of dog in French because it translates to "b****"? or is that only spanish
No, not only Spanish, but in any event the slang meaning of "chienne" would only be used for a (very bad) woman or girl. No confusion in a sentence like the one at the top, where you are clearly talking about animals.
Since the statement is specifically differentiating the dogs by gender, the best translation would say "The female dog is eating, the male dog is drinking" since English doesn't have a single word for a male dog.