Would you consider Wild Wild West to be a Weird West movie?

When I was thinking about starting this Lemmy community, I tried writing down every single Weird West work I'd seen, read, or played. In that list, I added Wild Wild West. But now that I think about it, I'm not sure if I'd call it a Weird Western.

Most Weird West works involve some sort of supernatural or fantasy element added to a Wild West setting. But does steampunk count as supernatural or fantasy? I mean, technically there weren't any giant steam-powered spiders in the Wild West but is that "weird" enough to qualify? The fact that it was steam-powered makes it harder for me to call it sci-fi. Besides, if I call Wild Wild West a Weird Western, does that mean Back to the Future Part 3 is a Weird Western too? I'm at the point where I'm questioning the definition of the genre to determine whether or not to post something.

Here's a trailer, and I'm sorry if watching it gets that theme song stuck in your head. The movie isn't streaming anywhere though.