Depends on what "Western elements" are. Heck, The Cage
even has a horse in it and Pike is wearing jeans!!!!!
But on a more serious note, it has Pike fighting the Kaylar and choking a shapeshifting Talosian. He also threatens to blow the Talosian's head off and the crew uses a laser canon to blow the top of a mountain off. Its not exactly an hour of navel gazing. Both pilots feature "ESP" with the Talosians illusion powers and Gary's telekinesis. Both have their talky elements. Both even have "ice queen" characters. Both have captains in conflict. Pike over staying in the service and Kirk over having to kill his best friend. I've never been quite sure why The Cage
is more "cerebral".