There's no doubt humans possess some powers (though certainly not godlike) that other organisms don't, but the distinction seems to be binary. E.g. the intelligence of dolphins, apes, and some birds doesn't seem to offer them any special control over other organisms (and it didn't even before humans arrived). So even if there could be such a thing as superhuman intelligence, I don't think it's reasonable to assume it could achieve control over humans (now superhuman charisma may be another matter).
"Destruction" is only one power that could be a component of "godlike power". There are several more; like power of intentional selective breeding, power of species creation (also via intentional selective breeding), etc.
What about power of granting happiness or misery to large swathes of a species (chickens, anyone?)
Oh, wait, that's not an animal. My bad.