Thor, Hebrew is a different language. In other langauges, words can mean more than one thing. Same as here. There are English terms that mean more than one thing, and there are terms in other languages which have no precise translation.
Take our word "love." Love can be charitas, agape, phileo, etc,...but we just say "love" for liking something, sex, physical desire, parental and brotherly love, the whole works.
To say, well, the Bible says "fish" is totally absurd. The Bible does not say "fish." "Fish" wasn't even a word back then. The Bible says a Hebrew word translated as fish, which is a good approximation.
Same with bird and bat. The same term refers to both.
Moreover, it's pretty clear that God intended and did grant man dominion over all life on earth. The fact every single life form is not mentioned is irrevalent.