Oh for sure!I won't make a strict line by line case, but the feel of a D&D party has more of John Wayne than Mallory.
Yeah, if you're putting it on a sliding scale with, say, Westerns on one end, and Arthurian romance on the other, most D&D, hell most fantasy (TTRPG or literary) is a lot closer to Westerns. I mean, a Wizard of Earthsea is more a Western than it is an Arthurian romance. Lord of the Rings is maybe midway between them on that scale (in part because Tolkien, that naughty boy, decided Arthurian stuff was "un-English").
But if you keep testing D&D on other sliding scales between Western and and other genres, like say, Pulp, or Road Trip, or Heist, or whatever the hell genre The Fast and The Furious has become (because it does seem like that is a genre), or like, Shonen anime (which even when set in the Wild West tends to defy the genre norms - I mean, Trigun is far less of a Western than Cowboy Bebop - note Cowboy Bebop isn't Shonen, per se), then I think you'll see more complex picture emerge. Eventually if you keep doing this with genre pairs, I think you'll find there's only a limited amount of Western influence in modern D&D, especially as it attempts to avoid sliding into problematic tropes.