He invented his own Poe style, which I'm sure was influenced by whatever ideas people had about good stories at the time, but he brought his own interpretation to it. It sounds like people remember Poe's interpretations and those became stories that defined those genres, with a nod to whatever came before it.

I think it’d be fair to call him the Stephen King of his day.

On the singular scale of "influential," I think that maybe popularity matters more than whatever he "invented," but he was indeed very, very popular.