I would suggest that an atheist who believes humans "deserve a higher place in the world than animals, as if we are divine beings" is deeply confused
It's funny you should say that though, as I tend to view that sense of superiority you're talking about as stemming pretty much directly from the Abrahimic faiths. Most other cultures seem to have developed a firmer grasp of their place within and as part of the natural world rather than separate from and somehow superior to it.
To get back somewhere near ot, one of the direct benefits I would expect to see from pursuading large numbers of people of god's non-existence would be a reduction in our over-inflated sense of self-importance.
This idea of us being god's chosen people is not just nonsense but dangerous nonsense, particularly if you happen not to be human.
BTW, animals do have rights