I think some cats are different because they are antisocial and there aren't that many of them. Compared to humans (and e.g. dogs) that have to hunt but also feed a group and support a social structure. Social cats like lions I believe do mostly eat bigger game. But cats overall are also extremely smart compared to most animals. Look into how intelligent tigers are. But they dont collaborate so they don't need that side of intelligence.

I do like your idea about the extant hunter gatherers, that should be easy to confirm.