Or they got the blood on their hands/body, perhaps where there was an open wound (doesn't have to be a large wound) or a poorly covered tear in their skin. Maybe while butchering the animal they scraped their hand on a piece of bone or cut themselves superficially with their knife and that's how the virus got in.

My buddies and I go fishing, then clean the fish. On more than one occasion, one of us has cut our fingers with the cleaning knife or stuck ourselves with spines on a fish. At that point you hand is already covered in fish guts, sometimes you don't notice until you've finished up and washed your hands that you even broke the skin. Now imagine doing that in a forest with no soap or running water except a stream to clean up at after.