Earth is already a game preserve in a vast Gallactic Empire.
The Grey guys in saucers are like the Park Rangers. They abduct folks and implant devices for the same reason we tag birds and fish. To keep track of us humans, and our migration patterns, and so on, so they "tag" individual humans and then release them back into the wild. And then follow up by recapturing them.
Earth almost got flattened so they could build a Walmart in its place. But the galactic equivalent of Walmart got put out of business by their equivalent of Amazon. So our nature preserve got...preserved! Whew!